An incisive passing move down the left flank involving Nicklas Bendtner and Gael Clichy allowed Denilson to pull the ball back from the byline for the France midfielder to pick his spot beyond Scott Carson.
The Gunners had a good chance to go further ahead just two minutes later when they had a solid claim for a penalty box handball, but referee Howard Webb's line of sight was obscured.
William Gallas shaved the outside of the post with a thunderous 30-yard drive after 11 minutes and Tony Mowbray's Premier League newcomers were well and truly under the cosh.
Arsene Wenger stated prior to the game that he was wary of playing against newly-promoted clubs, particularly in the opening game of the season.
However, West Brom seemed shell-shocked and overwhelmed by the occasion.
The newcomers to the top-flight had top-scored their way to promotion, but had also leaked almost as many at the other end so, given the start to the match, Baggies fans must have feared the worst.
The Midlands side appeared to weather the storm and the Gunners were limited to some long-range shooting, the most dangerous of which was Bacary Sagna in the 18th minute.
Wenger would not have been disappointed though as his side looked comfortable and enjoyed in excess of 70 per cent of possession during the opening half.
Bendtner should have doubled Arsenal's lead on 24 minutes when he rose unmarked to meet an inswinging Nasri corner, but the tall Dane headed the ball wide.
Manuel Almunia was called into action for the first time just before the half-hour when Kim Do-Heon ran on to Ishmael Miller's flick before drilling a low shot toward the left-hand side of the goal forcing the Spanish keeper to turn the ball away for a corner.
Mowbray's side began the second half with renewed conviction and, within minutes of the re-start, Almunia and Johan Djourou made vital saves to keep their side in the lead.
The Spaniard first blocked Miller's drive from the left after the powerful striker muscled past Djourou and then the Swiss defender blocked the rebound effort from Kim.
Emmanuel Adebayor looked certain to score in the 52nd minute but, as Carson came out to block, he tried to curl a shot inside the post across the keeper's body but the ball rolled wide of the target.
Substitute Robin van Persie forced the first save of the second half from Carson with a tame header from close range from Adebayor's lofted cross on 80 minutes.
The Netherlands striker almost created another moment of magic six minutes later with a shot from the outside of his left boot that flew narrowly wide.
West Brom grew in confidence during the second half and, although they did not create many chances, they kept possession better and will take heart from their first match back in the big time.