Verstappen took a grid penalty at the previous race in Russia and finished second after starting at the back of the field, his progress helped after late rain caused problems for others.
The six times world champion took the chequered flag at Imola 5.783 seconds ahead of team mate Valtteri Bottas, who started on pole position.
Max Verstappen leads Red Bull front row sweep in Bahrain
'I don't feel like I'm at the end. The next eight months or so I'll find out whether I'm ready to stop or not, I don't think I will personally, but you never know.'
Leclerc had seized the lead at the start, and held it through an initial safety car period, before Verstappen made up for his poor getaway and passed the Monegasque -- whose tyres were fading fast -- with a late move around the outside.
The victory on a hot afternoon at Le Castellet was Verstappen's seventh of the season and 27th of his career.
Nico Rosberg had his Formula One world championship lead over Mercedes teammate Lewis Hamilton cut to one point after the German was demoted from second to third place in the British Grand Prix on Sunday.
Dutch Formula One driver Giedo van der Garde dropped his legal action against Sauber, allowing the team to race in this weekend's season-opening Australian Grand Prix without him.
Team boss Christian Horner said Verstappen's lap of one minute 22.109 seconds was one of his best of the year and the Dutch driver sounded remarkably relaxed given the amount of pressure on him.
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.
Formula One leader Max Verstappen passed Mercedes rival Lewis Hamilton on the penultimate lap to win a tense French Grand Prix for Red Bull on Sunday and canter 12 points clear at the top.
Max Verstappen won the first sprint race of the Formula One season at the Chinese Grand Prix on Saturday.
Red Bull's Max Verstappen sang "Viva Las Vegas" after racing to a record-extending 18th victory of the season and joining Sebastian Vettel in third place on Formula One's all-time winners' list.
'I could never have dreamed of being where I am today.'
Germany's Nico Rosberg celebrated a surprise hat-trick of Monaco Grand Prix victories on Sunday after Mercedes blew championship-leading team mate Lewis Hamilton's chances with a needless pitstop.
Formula One leader Lewis Hamilton ousted Mercedes team mate Nico Rosberg from the top of the timesheets in Italian Grand Prix free practice on Friday. The Briton, chasing his 50th grand prix win on Sunday, enjoyed a sunny afternoon at the Monza circuit with a fastest lap of one minute 22.801 seconds on the supersoft tyres after being second to Rosberg in the morning. Rosberg quickest effort then was a 1:22.959, with the German lapping in 1:22.994 after lunch.
A summary of sports events and sports persons, who made news on Saturday
Hamilton's team mate Valtteri Bottas finished third, ahead of Ferrari's Charles Leclerc, in a race aimed at providing more thrills for fans over the three days of track action and potentially shaking up the starting grid.
Verstappen led from start to finish at Austria's Red Bull Ring, with seven-time world champion Hamilton second for Mercedes.
Maya Weug will be given a season in the FIA-sanctioned Formula Four championship.
IMAGES from the Azerbaijan F1 Grand Prix held at Baku City Circuit on Sunday
The Singapore Formula One Grand Prix has been cancelled for the second year in a row due to the COVID-19 pandemic.
Ferrari's Sebastian Vettel, winner of 52 races, has gone more than a year since he tasted victory at last year's Belgian race.
Formula One world champion Max Verstappen won the inaugural Miami Grand Prix for Red Bull on Sunday, slashing Ferrari rival Charles Leclerc's overall lead from 27 to 19 points after five races.
Indian shuttler Ajay Jayaram notched up a stunning three-game victory over higher-ranked Japanese Sho Sasaki to reach the men's singles semifinals of the Korea Open Super Series badminton tournament, in Seoul, on Friday.
Dutch Formula One driver Max Verstappen collected two special awards for the second year in a row at the International Automobile Federation (FIA)'s gala prize-giving ceremony on Friday.
Max Verstappen put Red Bull on pole position for the Canadian Grand Prix with Alpine's Fernando Alonso leaping onto the front row alongside the Formula One championship leader in a wet qualifying on Saturday.
Formula One title rivals Lewis Hamilton and Max Verstappen took each other out of the Italian Grand Prix on Sunday, with Mercedes team boss Toto Wolff slamming the incident as a 'tactical foul'.
Verstappen's hopes of a record-extending 11th successive victory looked a long shot on a city circuit where overtaking is never easy.
Red Bull's Dutch 20-year-old Max Verstappen took the chequered flag in second place with Kimi Raikkonen completing the podium for Ferrari and Australian Daniel Ricciardo finishing fourth for Red Bull.
Nico Rosberg eased to victory at the Japanese Grand Prix on Sunday with a drive that handed Mercedes their third straight constructors championship and extended the German's lead in his pursuit of a maiden Formula One title.
Lewis Hamilton can become only the third driver to win 50 grands prix when Formula One returns from its month-long August break and gets back to business at Sunday's Belgian Grand Prix.
Max Verstappen celebrated his 21st birthday in style on Sunday with the Red Bull driver carving from the back of the Russian Grand Prix grid to first in the space of 19 laps.
Finland's Valtteri Bottas seized the first Formula One victory of his career at the Russian Grand Prix on Sunday after jumping both Ferraris at the start and then holding his nerve over the tense closing laps.
Six-times world champion Lewis Hamilton and his team will take centre stage, hoping for another year of dominance after winning both titles for the past six years and ending up fastest in winter testing. Ferrari can be trusted to provide plenty of headlines with four-times champion Sebastian Vettel fighting to reassert himself at the team after being outshone by quick newcomer Leclerc, a double winner in 2019.
Lewis Hamilton took pole position at the Italian Grand Prix for the third year in a row on Saturday with Mercedes team mate and title rival Nico Rosberg joining the Briton on the front row of the grid.
Lewis Hamilton's world championship defence got off to a flying start on Sunday with a crushing victory for Mercedes in the season-opening Australian Grand Prix as Formula One rivals succumbed to a farcical rash of reliability problems.
Formula One teams say they will race in Russia, despite the crisis in Ukraine and downing of a Malaysian airliner, unless the country's debut Grand Prix in October is called off or they are ordered not to go.
IMAGES from the Silverstone F1 GP on Sunday
Max Verstappen won Red Bull's home Austrian Grand Prix from pole position and with the fastest lap on Sunday for the team's 10th successive Formula One victory and ninth in nine races this season.
