The Gunners looked set for victory as the Cottagers struggled to break down their makeshift defence and level Laurent Koscielny's 21st-minute header.
However, Johan Djourou's sending-off 12 minutes from time reduced Arsenal to 10 men and Steve Sidwell equalised before Zamora struck a late winner.
Earlier, Frank Lampard struck in the 89th minute to hand Chelsea a first win in five league matches at Wolves on a day when all four of the 1500 kick-offs went the way of the away teams.
Ramires put the Blues in front with a powerful 54th-minute effort but the hosts looked to have salvaged a point when Stephen Ward tucked away Steven Fletcher's lay-off with six minutes remaining.
But Lampard, who has had to get used to playing a less regular part this season, gave under-pressure boss Andre Villas-Boas a big boost when he converted Ashley Cole's cross just before the close.
Elsewhere, captain Joey Barton opened the scoring but was sent off as his QPR side slumped to a 2-1 defeat against Norwich in the battle of two of last season's promoted sides.
Barton had put his side, now winless in eight matches, in front after 11 minutes when he drilled home from the edge of the penalty area following Clint Hill's pass.
But the former Newcastle midfielder's joy soon evaporated when he was dismissed for an apparent headbutt on Bradley Johnson.
Anthony Pilkington levelled with a superb strike four minutes from the break. Substitute Steve Morison sealed the points in the 83rd minute following more good work down the left by Pilkington.
Blackburn, hot on the heels of their remarkable 3-2 win at Manchester United, were brought back down to earth by Stoke, who were 2-1 victors at Ewood Park.
Peter Crouch scored twice to put Stoke in control, bringing down crosses from Dean Whitehead and Matthew Etherington before finishing powerfully on each occasion.
Rovers came back into it when David Goodwillie grabbed his second goal for the club by stabbing over the line in a goalmouth scramble but there was no leveller.
Swansea made light of their poor form on the road to see off hosts Aston Villa 2-0.
Nathan Dyer started the scoring in the fourth minute, tucking the ball away right-footed from the edge of the area via a small deflection.
The Welsh side were rewarded for some attractive attacking play with a second goal in the 47th minute as Wayne Routledge lashed home after Danny Graham's shot had come back off the post.
Monday's Premier League Results
Fulham 2-1 Arsenal
Wolves 1-2 Chelsea
Aston Villa 0-2 Swansea
QPR 1-2 Norwich
Blackburn 1-2 Stoke