Allardyce's Hammers had failed to win any of their previous seven home league matches, but they finally gave the Upton Park faithful something to shout about as Ricardo Vaz Te's hat-trick inspired a sublime display on Saturday.
West Ham's morale-boosting first home win since February 4 lifted them to within three points of second placed Southampton -- who were beaten by Reading on Friday -- and the race for promotion to the Premier League looks sets to go down to the wire.
"We are in the race still and we have closed on Southampton's goal difference which could be a factor," said Allardyce, who believes his side could go up if they win their final three matches.
"We're still feeling the pressure as we have no margin for error. It's got to be three wins and then we can see if anyone has slipped up.
"We have to make sure we still have automatic promotion to play for on the last day against Hull."
Former Barnsley winger Vaz Te started the rout with two goals in the first eight minutes before skipper Kevin Nolan added the third by the 11th minute.
Vaz Te struck again with a superb scissor kick just after the hour mark to take his tally to five goals in his last two matches.
Carlton Cole added the fifth and Brighton's misery was complete when Gary Dicker put through his own net.
Doncaster manager Dean Saunders slammed referee Mick Russell after he saw his side relegated to League One following a 4-3 defeat against Portsmouth.
Rovers scored twice in the opening five minutes but the match turned on the controversial dismissal of Habib Beye, who gave away a penalty despite appearing to make minimal contact with Dave Kitson outside the area.
Beye saw red as the last man and, moments after Greg Halford tucked home the penalty, Russell awarded a second dubious spot-kick for handball against James O'Connor.
While James Coppinger fired Rovers back ahead soon after, a chaotic end to the match saw Kitson level in the 90th minute, despite appearing to shovel the ball across the line with his hands, before Markos Futacs grabbed the winner in stoppage-time.
"I don't know if you've seen them all but that's Billy Smart's Circus out there, all four goals," Saunders said.
"I just hope the referee recovers from that. I just can't see him recovering from it. His career. The assessor was there.
"Let his boss who is above him and the assessor make that decision as to whether he referees ever again."
Coventry fill the final relegation place after a 1-1 draw at Burnley left Andy Thorn's side four points from safety.
It could have been worse for Coventry, but fourth bottom Bristol City were unable to hold onto a two-goal lead in their 2-2 draw at Birmingham.
Fifth placed Blackpool were held to a 0-0 draw at Nottingham Forest, while Cardiff are sixth following their 1-0 win at Barnsley.
It stretched Cardiff's unbeaten run to seven games and moves them two points clear of seventh-placed Middlesbrough with three games to go.
Middlesbrough remain in the hunt for the play-offs after a 1-0 win at Derby.
In the day's other matches, Leeds beat Peterborough 4-1, Millwall beat Leicester 2-1, Crystal Palace drew 1-1 with Ipswich and Watford shared a 1-1 draw with Hull.
Source: AFP
Source: AFP