The Gunners captain quickly passed to Hleb, who drilled a low shot past Helton.
On 23 minutes the Gunners went ahead with a fine build-up and neat finish by Hleb.
In addition, Alex Hleb will spend a season on loan at the Italian club.
Arsenal nearly added a third when Fabregas poked a shot wide after excellent play by Hleb.
But his low penalty was saved close to full-time after Alexander Hleb was tripped in the area.
The visitors had taken a first-half lead when Stephen Crainey's error gifted a goal to Alexander Hleb.
Inter coach Roberto Mancini has confirmed Hleb is one of the players the Italian club "would like to sign".
But Wenger insists that Hleb is still part of his plans and wants him to stay at the club.
For Arsenal, Alexander Hleb hit the side netting, and Baptista shot tamely at James before wasting another free header.
BBC: Portsmouth and Arsenal found each other hard to break down
The visitors then lost McShane for a wild tackle on Hleb before Walcott hit a post in the dying seconds.
Brmingham manager Alex McLeish had intended to withdraw Alexander Hleb in place of striker Nikola Zigic but opted to replace Bowyer instead.
Gilberto's move means three midfielders have left Arsenal this summer, with Alexander Hleb (Barcelona) and Mathieu Flamini (AC Milan) also moving out.
They were level six minutes later, however, when Van Persie crashed in from the penalty spot after Gary Cahill brought down Hleb.
Pogrebniak then hit the post from close range after the impressive Hleb had robbed teenage defender Danny Wilson in the Rangers penalty area.
And City's brave resistance was finally ended when Hleb jinked his way into the penalty area and his cross was converted by Baptista.
The Gunners had strong shouts for a penalty waved away by ref Styles when Alexander Hleb appeared to be taken down by Spector.
Arsenal manager Arsene Wenger said that Nasri had "great potential" and could now allow unsettled Belarus international Alexander Hleb to leave the Emirates Stadium.
But he and his Rovers team-mates quickly became overrun in midfield with Cesc Fabregas, Hleb and Gilberto pulling the strings as Arsenal took control.
With Alexander Hleb at the heart of everything, the German side fizzed first-time passes across the rain-sodden pitch, cutting through the home ranks with alarming ease.
However, Hleb, who scored his first Blues goal against Milton Keynes Dons in the Carling Cup in midweek, dragged his volley wide of the far post.
Wenger's side nearly retook the lead when first Emmanuel Adebayor's effort was well saved by Isaksson and then Alexander Hleb flashed a left-footed strike just wide.
Stuttgart coach Markus Babbel awarded Alexander Hleb and Pavel Pogrebnyak immediate debuts in his starting side less than a week after the pair joined the club.
Midfielders Alexander Hleb and Cesc Fabregas were busy in the middle but their energy was matched by Boro's midfield, with George Boateng and Gary O'Neil particularly outstanding.
At the other end, Hleb released Jerome, who recovered from an initial stumble to fire a shot, which was well parried by Kingson at his near post.
He burst into the box to get on the end of Hleb's pass and drove in a low shot that Pepe Reina could only help into the net.
The hosts handed Alexander Hleb, on a season-long loan from Barcelona, his home Premier League debut and the Belarus international could have opened the scoring inside two minutes.
Until, that is, Arsenal went wide as Hleb floated over a pin-point cross from the right for Adebayor to power home a header past a helpless Antti Niemi.
Suddenly the Gunners were rampant, with their pass-and-move game causing Bolton all sorts of problems, and Alexander Hleb should have extended the lead when he poked wide from 16 yards.
Barcelona manager Pep Guardiola made late changes to try and win the game and both his substitutes, Bojan Krkic and Alexander Hleb, could have given the Catalan giants a late victory.
Stefan Klos was out to make a point after being frozen out of the German international squad and made a great save to block at the feet of Stuttgart's Alexander Hleb.
BBC: SPORT | Football | Champions League | Rangers stun Stuttgart
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