Fernando Torres fired Chelsea ahead following some poor marking by Laurent Koscielny and Juan Mata's free-kick squirmed in to secure three points for the European champions after Gervinho had equalised on the stroke of half-time.
Former England skipper Terry was earlier this week found guilty of using racist language towards Anton Ferdinand by a Football Association hearing, but is awaiting the full written judgment of the independent panel, before deciding whether to appeal a verdict which saw him banned for four matches and fined £220,000.
The 31-year-old has always protested his innocence and was found not guilty of a racially aggravated public order offence in a criminal trial during July.
Predictable chants of "you know what you are" from the Arsenal crowd greeted Terry's first touch, as did jeers for former Gunner Ashley Cole.
However, the Emirates Stadium faithful had little to sing about as the match wore on.
While Chelsea came through their first real test of the new campaign, the Gunners again saw question marks raised over their defensive resilience.
Arsenal had made a lively start, with Ivory Coast forward Gervinho again deployed down the centre as contract rebel Theo Walcott watched on from the bench.
On 11 minutes, Abou Diaby created space for himself some 20 yards out and shot fiercely at Petr Cech.
However, the French midfielder's injury jinx appeared to strike again as he was soon replaced by Alex Oxlade-Chamberlain.
Chelsea took the lead on 20 minutes with a brilliant finish from Torres.
A free-kick from Mata on the right was floated through the Arsenal penalty area towards the far post.
Laurent Koscielny was wrestling with Torres, but the Spaniard was still able to hook the ball back into the net.
Before Arsenal could regroup, they were almost 2-0 down.
Torres robbed Koscielny out on the left and darted into the penalty area.
However, as the keeper came out and he shaped to shoot, the Spaniard tumbled, claiming his heel had been clipped by Koscielny.
Referee Martin Atkinson, however, was having none of it.
Slowly Arsenal found their rhythm again.
Gervinho was picked out at the far post and headed back across goal instead of at it.
The Gunners' frustrations were starting to show as Aaron Ramsey was booked for a late tackle on Oscar in the 35th minute.
The Brazilian then also went into the notebook after another poor challenge on Mikel Arteta, who played a key role in the Gunners' equaliser after 42 minutes.
Patient build up from right-back Carl Jenkinson fed the ball back to Arteta, and he slipped Oxlade-Chamberlain down the flank.
His low centre across the six-yard box was collected by Gervinho, who had sidestepped Terry, with his back to goal - and he turned to blast a shot into the roof of the net.
Arsenal started the second half brightly, with Santi Cazorla snatching at an angled drive which flew wide.
However, the Gunners were undone again in the 53rd minute.
Once more Mata's curling delivery caused panic in the Arsenal penalty area - and a backtracking Koscielny helped the ball on with the slightest of touches into the corner past Vito Mannone's dive.
Arsenal had to regroup again, and were almost level when Cech brilliantly palmed away a looping header from Lukas Podolski.
Wenger had seen enough and made a double change after 66 minutes, bringing on Walcott for Ramsey and Olivier Giroud, who scored his first Arsenal goal in the midweek Capital One Cup win over Coventry, for Podolski.
Cech was on hand to palm away a deflected effort from Giroud as Arsenal looked for the equaliser.
Gibbs tripped Mata on the edge of the penalty area to give Chelsea another dangerous piece. This time, though, his shot went straight into the wall.
As the match entered the final 10 minutes, Arsenal continued to press for an equaliser, but were frustrated by a combination of poor passing and determined defence.
Giroud had a golden chance to snatch an equaliser in stoppage time, but was forced wide by Cech and could only smash his shot into the side netting.
Terry made a point of heading over to the travelling support at the final whistle, handing his boots to a couple of young fans.