But the Premier League champions were handed a lifeline soon after half-time when Arsenal goalkeeper Manuel Almunia needlessly conceded a penalty that Wayne Rooney converted.
It got worse for Arsenal as French midfielder Abou Diaby headed a Ryan Giggs free-kick into his own net five minutes later to give United their third win in four games.
Arsenal´s visit to Old Trafford was seen as the acid test of Wenger´s young team and it started perfectly when Arshavin hit a swerving long-range shot that United goalkeeper Ben Foster could only push into the net.
But Almunia had a rush of blood in the 59th minute when he charged out and tripped Rooney.
United striker Rooney picked himself up to send Almunia the wrong way from the spot and Sir Alex Ferguson´s team won it five minutes later when Diaby diverted Giggs´s harmless free-kick past Almunia.
Robin van Persie thought he had equalised in the last minute of stoppage time but the Arsenal striker´s effort was ruled out for offside, leading Wenger to be sent to the stands as he complained furiously.
Elsewhere, leaders Chelsea maintained their blistering form with a 3-0 victory over Burnley, while Liverpool came from behind to beat 10-man Bolton 3-2.
Nicolas Anelka broke Burnley´s stubborn resistance at Stamford Bridge when he slid in to convert Didier Drogba´s cross just before half-time.
Promoted Burnley, who had claimed famous victories over Manchester United and Everton in their previous two matches, were then swept aside.
Michael Ballack added Chelsea´s second goal soon after the break when he headed in Frank Lampard´s cross and Ashley Cole smashed in the third five minutes later to give Carlo Ancelotti´s team a fourth successive victory under their new Italian manager.
At Bolton, Rafael Benitez´s Liverpool showed they have the stomach to fight for the title.
The Reds had made a spluttering start to the campaign, with defeats against Tottenham and Aston Villa raising questions about their ability to win the league for the first time since 1990.
They fell behind to Bolton in the 33rd minute when Kevin Davies punished poor marking to drive home from close-range.
Glen Johnson equalised with a powerful strike from the edge of the penalty area in the 41st minute.
Tamir Cohen restored Bolton´s lead two minutes into the second half. But Bolton´s Sean Davis was harshly shown a second yellow card for a foul on Lucas in the 55th minute.
The visitors took full advantage as Dirk Kuyt found Fernando Torres and the Spain striker finished smartly.
Steven Gerrard, criticised in the week by Benitez for his poor form, hit the winner with a perfectly-struck shot in the 83rd minute.
"It was the perfect response from the players," Benitez said. "You could see all the players, from the first minute, played with a lot of determination to win. It´s important to have this mentality."
Tottenham, in second place on goal difference, kept pace with Chelsea as Aaron Lennon´s last-gasp goal sealed a 2-1 victory over Birmingham at White Hart Lane.
Harry Redknapp´s team have made their best start to a season for 49 years and they chalked up win number four in dramatic fashion.
Peter Crouch put Tottenham in front after 72 minutes when the England international headed in Tom Huddlestone´s free-kick.
Lee Bowyer levelled for Birmingham just three minutes later when Alan Hutton and keeper Carlo Cudicini made a hash of clearing.
But Tottenham won it five minutes into stoppage time through England winger Lennon.
Dave Kitson´s first league goal for Stoke clinched a 1-0 victory over Sunderland at the Britannia Stadium.
Kitson, who cost 5.5 million pounds from Reading last year, lashed in Danny Higginbotham´s knock-down in the 43rd minute.
Wolverhampton are still waiting for their first home win of the season as Hull ground out a 1-1 draw at Molineux.
Brazilian midfielder Geovanni gave Hull the lead in the third minute, but Richard Stearman equalised in the 46th minute.
Blackburn and West Ham played out a dour goalless draw at Ewood Park.
English Premier League results on Saturday night:
Blackburn 0 West Ham 0
Bolton 2 (Davies 33, Cohen 47) Liverpool 3 (Johnson 41, Torres 56, Gerrard 83)
Chelsea 3 (Anelka 45, Ballack 47, A Cole 52) Burnley 0
Man Utd 2 (Rooney 59-pen, Diaby 64-og) Arsenal 1 (Arshavin 40)
Stoke 1 (Kitson 43) Sunderland 0
Tottenham 2 (Crouch 72, Lennon 90+5) Birmingham 1 (Bowyer 75)
Wolverhampton 1 (Stearman 46) Hull 1 (Geovanni 3)
Related story
Barcelona 2-1 Valencia: La Liga leaders break all-time unbeaten...
