The late goals followed Sunderland's last-kick winner over league leaders Manchester City on Sunday and maintained the unpredictability of the busy holiday programme with the race for the title and top four places still wide open.
Manchester City are top on goal difference from Manchester United with both clubs on 45 points from 19 games followed by Tottenham Hotspur in third on 39 having played one game less.
Chelsea are fourth on 37 points from 20 matches, one clear of Arsenal who slipped to fifth after having Johan Djourou sent off 12 minutes from time before Zamora's goal in the third minute of stoppage-time sent them crashing to defeat.
City host Liverpool, who are sixth, on Tuesday when Spurs take on mid-table West Bromwich Albion while Manchester United visit seventh-placed Newcastle United on Wednesday.
In Monday's other matches all the away teams won with Swansea City earning a 2-0 victory at Aston Villa, Stoke City beating Blackburn Rovers 2-1 and Norwich City winning 2-1 at fellow promoted club Queens Park Rangers who had Joey Barton sent off after he had earlier scored the opening goal.
Arsenal slipped one place to fifth after Chelsea's earlier win but seemed set to reclaim a top four spot having taken a 1-0 lead at Craven Cottage with the game moving towards its finale.
Laurent Koscielny put Arsenal ahead with a 21st minute header but Fulham, who lost 5-0 to Manchester United in their last home game, came back strongly in the second half.
They went close to equalising three times before Djourou was sent off for hauling back Zamora in the 78th minute which helped tip the match even more in their favour.
Steve Sidwell, who won the FA Youth Cup at Arsenal but never made the first team, finally headed Fulham level after 85 minutes before Zamora smashed in the winner with a slightly mis-hit left-foot volley with seconds remaining.
Fulham manager Martin Jol, who enjoyed his first Premier League victory over Arsene Wenger's side in nine attempts, told Sky Sports:
"It was amazing. It's a big compliment to all the players because in the second half they were on the front foot and to get the equaliser was a big boost.
"We played very well in the second half after they outplayed us for the first 20 or 25 minutes."
However, Jol's adversary from the Dutchman's days of managing Arsenal's arch-rivals Spurs was far from happy.
Wenger claimed Djourou should not have been sent off and that Arsenal should have had a penalty in the first half when Gervinho was tripped in the box.
"We went down to 10 men but in my opinion it was a foul for us on the second yellow for Djourou," Wenger said.
"We should have had a penalty in th
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.