Arsene Wenger admitted arsenal's Premier League challenge will take its toll on his health if they leave any more victories as late as they did at Hull City on Saturday.
Nicklas Bendtner scored in stoppage time to keep Arsenal level on points with Chelsea, although they have played a game more.
Arsenal had led through Andrey Arshavin, but Jimmy Bullard levelled from the penalty spot before George Boateng was sent off for Hull just before half-time.
"It's maybe not good for my heart, but for the championship it's not bad," Wenger said after Arsenal's fifth straight win.
"We have eight games to go, we are in there, why should we not believe?
"What I believe especially is that we will give absolutely everything to do it (win the title). You saw that in the game today. We were a bit jaded but we kept going.
"We needed the three points and we got it after the 90 minutes."
Chelsea had earlier thrashed West Ham 4-1. Alex headed the Blues in front on 16 minutes, only for Scott Parker to smash a 25-yard effort past goalkeeper Ross Turnbull and level against his former club.
However, Chelsea went back in front when Didier Drogba (55) headed in Florent Malouda's cross and the French winger capped a superb display when he netted a third with 13 minutes left.
Former Hammers man Frank Lampard hit the post before Ivory Coast striker Drogba scored his second in stoppage time.
At the other end of the table, Wolves put some distance between themselves and the bottom three with a 2-1 win at struggling Burnley.
Matt Jarvis (26) fired the visitors ahead after latching onto a poor back-pass from Tyrone Mears.
Clarets striker David Nugent saw his close-range effort bounce up on to the top of the crossbar, and Burnley's luck was out again when Clarke Carlisle deflected Adlene Guedioura's shot into his own net at the start of the second half.
Steven Thompson (73) set up a grandstand finish with a goal for the hosts, but Wolves held on to secure a much-needed victory.
With Wigan suffering a 4-0 thrashing at Bolton, Wolves have moved clear of the bottom three.
"It's tightened it up again with West Ham and Wigan losing and it gives us more of a fighting chance, a bit of confidence," said Wolves boss Mick McCarthy.
Burnley boss Brian Laws admitted the 2-1 defeat was hard to take but urged his players to forget the result and concentrate on the battle to beat the drop.
Laws said: "We feel a little hard done by but we've got to move on. It's a huge knock but the season doesn't end today and there are still eight games to go."
In the early kick-off, Tottenham maintained their hopes of a top-four finish as they beat Blackburn 3-1 at White Hart Lane with goals from Jermain Defoe and Roman Pavlyuchenko (two).
Birmingham fought back from 2-0 down to draw 2-2 against in-form Everton at St Andrew's, while Stoke and Aston Villa played out a 0-0 draw.