In a race of safety cars and surprises, Verstappen's former team mate Pierre Gasly made a first podium appearance in second place for Red Bull-owned Toro Rosso, a rare Honda-powered one-two.
Ferrari's Charles Leclerc held off Lewis Hamilton to win his first Formula One race on Sunday in the Belgian Formula One Grand Prix.
The victory at Suzuka was the Dutch driver's 13th in 16 races this season and left him on the brink of a third world title.
Images from the Tuscan F1 Grand Prix held at at Mugello, Scarperia e San Piero in Tuscany, Italy, on Sunday.
Norris said he had also been on pain-killers for a back problem and had not felt confident in the car, limiting his track time in the afternoon.
Hamilton said he had not been feeling well on Thursday and Friday, when he was also up until midnight working with his engineers.
Max Verstappen won the season opener as Red Bull registered a dream start with a one-two finish at the Bahrain GP.
Max Verstappen took pole position on Saturday in a wet qualifying for a Canadian Grand Prix
McLaren's Australian Daniel Ricciardo will join the Dutch 23-year-old on the front row for the first time since the pair were team mates at Red Bull in 2018.
It was the first time Verstappen, winner of a record 19 of 22 races last year, has won the first two races of a season. He has also won 19 of the last 20.
Lewis Hamilton lapped fastest overall for Mercedes in Hungarian Grand Prix practice
Charles Leclerc crashed at the end of qualifying for his home Monaco Grand Prix on Saturday
Max Verstappen won his home Dutch Grand Prix for Red Bull on Sunday and took the Formula One championship lead in front of a roaring, dancing army of fans hailing their hero with orange flags and flares.
Max Verstappen became the first Formula One driver to take 16 victories in a season
Max Verstappen took the 50th win of his Formula One career, and record-equalling 15th of the season
Charles Leclerc put Ferrari on pole position for Sunday's US Grand Prix after Red Bull's triple Formula One world champion Max Verstappen had a faster lap deleted for exceeding track limits and dropped to sixth on the grid.
Can Mercedes' seven-time world champion Lewis Hamilton add to his record tally of 103 victories?
Red Bull's Max Verstappen qualified third, after a power unit scare in the second phase sent mechanics scrambling to fix his car, with AlphaTauri's Pierre Gasly a stunning fourth on the grid.
The Briton's Finnish team mate Valtteri Bottas will line up alongside on the front row of the starting grid with Ferrari's Kimi Raikkonen and Sebastian Vettel behind them.
Max Verstappen won the Spanish Grand Prix from pole position to stretch his Formula One championship lead to 53 points.
Lewis Hamilton is now just three wins short of Ferrari great Michael Schumacher's all-time record 91.
Max Verstappen put Red Bull on pole position for Formula One's season-opening Bahrain Grand Prix on Saturday, with seven times world champion Lewis Hamilton alongside on the front row for Mercedes.
The Dutch driver won the race at Suzuka, with Leclerc demoted from second to third behind Red Bull's Sergio Perez for cutting the final chicane while defending from the Mexican on the last lap.
Max Verstappen dashed Ferrari's home hopes and won the Italian Grand Prix
Formula One championship leader Charles Leclerc took pole position for the inaugural Miami Grand Prix ahead of Ferrari team mate Carlos Sainz in a front row lockout in qualifying on Saturday.
Four days before the season-opening Australian Grand Prix, Horner said his team still had plenty of ground to make up, however.
Lewis Hamilton took his 98th career pole position in qualifying for the Bahrain Grand Prix on Saturday
Monaco's Leclerc, who had started on pole position for the first time, lost power with 10 laps to go while leading and finished third with an extra point for the fastest lap.
Formula One world champion Lewis Hamilton took pole for Mercedes at the season-opening Australian Grand Prix.
IMAGES from the Azerbaijan F1 Grand Prix held at Baku City Circuit on Sunday
Hamilton's 98th career victory, from his 100th pole position, was his third win in four races
Ferrari's Carlos Sainz won the Singapore Grand Prix on Sunday to end Formula One leader Max Verstappen's record run of 10 wins in a row.
Ferrari's Charles Leclerc secured pole position for the Singapore Grand Prix on Saturday after a furious Max Verstappen was forced to abandon his fastest lap for fear of running out of fuel.
'We've still got work to do to get both cars home in the points. We'll take positives from today, but we're trying to find a bit more every weekend.'
Sergio Perez won the Saudi Arabian Grand Prix from pole position in a Red Bull one-two on Sunday with Max Verstappen staying top of the championship after racing from 15th to second.
Max Verstappen led a soggy Monaco Grand Prix from start to finish on Sunday
IMAGES from the Belgian F1 Grand Prix
Hamilton held on for fourth, but slipped from 18 to 32 points behind Verstappen in the championship standings.
Lewis Hamilton, who started on pole position in Sochi hoping for a 91st Formula One victory to equal Ferrari great Michael Schumacher's all-time record, finished third behind Red Bull's Max Verstappen.
The pole was the 95th of Hamilton's career and seventh in nine races this season, continuing Mercedes' 100% record in qualifying.
