Red Bull are hoping that engine and chassis upgrades will help them beat Ferrari and Formula One champions Mercedes more often after Max Verstappen's Spanish Grand Prix victory on Sunday.
Piastri now leads Britain's Norris by 14 points with five rounds and two sprints remaining, while Verstappen has slashed his gap to the Australian to 40 after being 104 behind at the end of August.
Red Bull's Max Verstappen secured a dominant win from pole position in the Azerbaijan Grand Prix in Baku, leading the race from start to finish.
Mark Webber was fastest for champions Red Bull in Formula One testing in Barcelona on Thursday with the Australian becoming the ninth driver to top the timesheets in as many test days so far this year.
"To expect them to win a Grand Prix is a pipe dream at this moment in time," said the Scot, winner of 13 races with Williams and McLaren.
Four times Formula One world champion Sebastian Vettel decided to leave Red Bull because he needed new motivation after a frustrating season, team consultant Helmut Marko said.
Red Bull are among a number of team frustrated by their inability to keep up with Mercedes, who dominated Formula One last year and cruised to an easy victory in Sunday's season-opening Australian Grand Prix
Red Bull expect Sebastian Vettel to help team-mate Mark Webber win the Formula One world championship should the situation arise but will not be ordering him to do so.
Sebastian Vettel's 'stab-in-the-back' Malaysian Grand Prix win revived an age-old debate about team orders in Formula One but trust, or the lack of it, could be more of a headache for champions Red Bull in the weeks ahead.
Rampant Red Bull charged to a front row sweep in Melbourne on Saturday with Sebastian Vettel denying disappointed team mate Mark Webber pole position for the Australian's home Grand Prix. The German, still only 22 but heavily fancied for this year's Formula One title, lapped Albert Park's tight street circuit in one minute 23.919 under overcast skies for his second pole in two races.
Red Bull have taken back total control of the Toro Rosso Formula One team, the energy drink company said on Tuesday. The company said in a statement that they had re-acquired co-owner Gerhard Berger's 50 percent holding "subject to approval by competition authorities".
Mark Webber charged Red Bull with emotionally favouring Formula One team mate and title rival Sebastian Vettel on Thursday and said his own championship challenge had been "inconvenient".
Switzerland's Sebastien Buemi will start his fifth year as Red Bull reserve driver next season, the Formula One team said on Tuesday.
A limping Mark Webber helped unveil the new Red Bull Formula One car on Monday that could allow the Australian to step up alongside new team mate Sebastian Vettel as a race winner this season.
Red Bull joined champions Ferrari in agreeing to extend Formula One's existing commercial agreement to 2012 and turning their backs on a rival series.
Formula One champions Red Bull expect Mark Webber to be back up to speed in Malaysia this weekend after modifications to his car, team principal Christian Horner said on Monday.
Red Bull set a Formula One record of 16 pole positions in a season when double world champion Sebastian Vettel lapped fastest in qualifying for the inaugural Indian Grand Prix Saturday.
The 34-year-old's contract expires at the end of the year and he has said he is most likely to stay with the team or retire rather than drive for anyone else.
Red Bull's Formula One world champion Sebastian Vettel put down a marker for a possible fifth win in a row by dominating both practice sessions for the Chinese Grand Prix on Friday.
Formula One champions Red Bull have changed their split-second pitstop procedures after a rear wheel flew off Mark Webber's car in the pitlane in Germany last weekend and injured a television cameraman.
A weekend that began at the top of the timesheets for Max Verstappen ended with the Dutchman out of the points and in a war of words with Ferrari rivals after a nightmare Belgian Formula One Grand Prix.
Red Bull made a formal protest at the Monaco Grand Prix on Sunday after it emerged that Mercedes, who swept the front row in qualifying for the Formula One race, carried out a secret tyre test with Pirelli last week.
Sebastian Vettel has been backed by his Red Bull principal to get even better as a driver having become the youngest triple Formula One World Champion in the season-ending Brazilian Grand Prix on Sunday.
Red Bull dropped Daniil Kvyat to sister team Toro Rosso following his disastrous weekend at the Russian Grand Prix and promoted Max Verstappen as his replacement ahead of the Spanish Grand Prix.
Outgoing Formula One champion Sebastian Vettel and Australian team mate Daniel Ricciardo were sent to the back of the grid at the season-ending Abu Dhabi Grand Prix on Saturday after stewards ruled Red Bull had used an illegal front wing.
The two McLaren drivers were ruled out for excessive skid plank wear hours after the race had ended and the podium champagne been sprayed.
Ferrari need to burst from the blocks next year to inject some much-needed rivalry into Formula One after a 2011 season which has turned into a one-man show starring Sebastian Vettel, Fernando Alonso has said.
Lewis Hamilton led a Mercedes 1-2 at the top of the timesheets for the first free practice session at the season-opening Australian Grand Prix on Friday, while McLaren's hopes of a clean start were tempered by reliability issues.
Red Bull were talking to Volkswagen about a Formula One partnership before a diesel emissions scandal seemingly scuppered plans, team boss Christian Horner said on Friday.
Red Bull are pinning their hopes that a calculated gamble that may have ended the team's run of pole positions will deliver them victory in Sunday's Canadian Formula One Grand Prix.
The four-time world champion was summoned after the second session at the Hungaroring as stewards reviewed the video evidence.
Mocked, misjudged, written off, Lando Norris's carves own road to F1 Glory
Austrian Christian Klien will race the next four Grands Prix for Red Bull and probably the two after that as well
Italian test driver Vitantonio Liuzzi has led the way for Red Bull in Australia with the fastest time in a low-key first practice session of the 2005 Formula One season.
Max Verstappen suffered his first retirement of the Formula One season on Sunday after a collision with Mercedes' Kimi Antonelli on the opening lap of Red Bull's home Austrian Grand Prix.
Formula One's pre-season mind games kicked off on Tuesday with Fernando Alonso having a dig at Red Bull after one of Sebastian Vettel's main mentors accused the Ferrari driver of playing politics last year.
Sebastian Vettel and Mark Webber could both be accused of losing their grip on Friday after the Red Bull duo launched scathing attacks on what they perceive as tyre wear becoming too dominant a factor in Formula One.
Red Bull, drivers' and constructors' champions for four years in a row from 2010, have fallen out with underperforming Renault and are casting around for a replacement engine provider with Ferrari their only real option given Honda's woes.
World champion Sebastian Vettel will start the Formula One season-opener from pole position on an all-Red Bull front row later on Sunday after posting the fastest time in the rain-delayed qualifying for the Australian Grand Prix.