The German, whose last victory was in Belgium in August 2018, took the chequered flag 2.641 seconds ahead of Monegasque team mate Charles Leclerc, who had started on pole position for the third race in a row.
Max Verstappen won the Spanish Grand Prix from pole position to stretch his Formula One championship lead to 53 points.
Formula One leader Lewis Hamilton put Mercedes on pole position for their 200th race at the German Grand Prix on Saturday while engine problems dashed Ferrari's hopes.
Ferrari won the race in one-two formation, with Sebastian Vettel leading Charles Leclerc, for their third successive victory.
Verstappen, who is 145 points clear of team mate Sergio Perez in the championship and set for a third title well before the end of the season, suggested Wolff should focus on his own team.
Lewis Hamilton dominated Sunday's Hungarian Grand Prix from pole position, with a bonus point for fastest lap, to take a five point lead over Bottas, the winner of the Austrian season-opener.
It was Hamilton's first pole position since Saudi Arabia in December 2021.
The Saudi Arabian Grand Prix is the penultimate race on this year's Formula One calendar
Seven-times world champion Lewis Hamilton won the inaugural Qatar Grand Prix for Mercedes on Sunday to cut Max Verstappen's overall Formula One lead to eight points with two races remaining.
Max Verstappen fought back from a slow pitstop to win the US Grand Prix in Austin on Sunday as his Red Bull team clinched the Formula One constructors' title a day after the death of billionaire owner Dietrich Mateschitz.
Formula One will have a record 24 races in the season that starts in Bahrain on Saturday.
Max Verstappen took pole position on Saturday in a wet qualifying for a Canadian Grand Prix
Formula One's 'halo' head protection device makes its race debut this season in a 21-round championship with France and Germany back on the calendar and some new faces joining the old favourites on the starting grid.
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.
Mick Schumacher, who will face intense scrutiny as embarks on his Formula One career, said for now he was simply overwhelmed to be following in his father's footsteps and called his promotion a dream come true.
Six time world champion Lewis Hamilton, winner of the British Grand Prix from pole position at the same circuit last weekend and 30 points clear of Valtteri Bottas after four races without spectators, was 0.138 seconds slower.
Max Verstappen led a soggy Monaco Grand Prix from start to finish on Sunday
Ferrari's Sebastian Vettel qualified third, ahead of 21-year-old Monegasque team mate Charles Leclerc who was unable to repeat his Bahrain Grand Prix pole of two weeks ago.
Max Verstappen won the Miami Grand Prix from ninth on the starting grid with a masterful display of tyre management on Sunday.
Ferrari's Charles Leclerc qualified third with team mate Sebastian Vettel a distant seventh on a distinctly off day for the German.
Ferrari's new team principal Mattia Binotto said earlier in the year that Vettel, as the team's "champion", would be given priority over Leclerc in certain racing situations, though he later clarified the drivers would be "free to fight".
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.
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.
IMAGES from the Belgian F1 Grand Prix
Lewis Hamilton is now just three wins short of Ferrari great Michael Schumacher's all-time record 91.
Sebastian Vettel has never been one for social media or had much time for esports but even the four-times world champion has shifted his stance, however slightly, under Formula One's coronavirus lockdown. Although the 32-year-old Ferrari driver is still not remotely tempted by Twitter or Instagram, he has acquired a gaming rig. Just how much the German uses it remains to be seen.
Sebastian Vettel was Ferrari's first choice to stay and partner Charles Leclerc in Formula One next year until the COVID-19 pandemic changed everything, team principal Mattia Binotto said on Friday. The four-times World champion, who won his titles with Red Bull, will now be replaced by Spaniard Carlos Sainz who joins from McLaren at the end of the season in a decision announced in May.
Verstappen led from start to finish at Austria's Red Bull Ring, with seven-time world champion Hamilton second for Mercedes.
Daniel Ricciardo is of Italian descent and has long been considered an obvious target for Ferrari,
Valtteri Bottas ended his year-long drought with a dominant victory in Turkey on Sunday while unhappy Mercedes team mate Lewis Hamilton finished fifth and lost the Formula One championship lead to Red Bull's Max Verstappen.
Lewis Hamilton took his 98th career pole position in qualifying for the Bahrain Grand Prix on Saturday
Hamilton's 98th career victory, from his 100th pole position, was his third win in four races
The front row lockout was a record-equalling 65th for champions Mercedes.
Lewis Hamilton lapped fastest overall for Mercedes in Hungarian Grand Prix practice
Max Verstappen clinched his second win of the season as the Australian Grand Prix was halted with three red flags.
Ferrari are planning to add female racers to their expanding young driver programme as they seek to develop talent for the future.
The times at the Istanbul Park circuit, hosting a Formula One race for the first time since 2011, were largely meaningless.
Red Bull's double World champion Max Verstappen won the Mexico City Grand Prix on Sunday to set a Formula One record of 14 victories from a single season, as well as the most points scored.
Red Bull's double World champion Max Verstappen swept to pole position at the Mexico City Grand Prix on Saturday with his sights set on a record 14th victory of the season.
Hamilton has won half of the season's 20 races so far, propelling his team to an unprecedented sixth successive title double, but Brazil was a disappointing weekend with Valtteri Bottas retiring.
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