Everton 2-1 Southampton
A superb 92nd-minute winner by Tomasz Radzinski gave Everton a deserved win against Southampton at Goodison Park.
James Beattie's 17th Premiership strike this season had put the visitors ahead but Everton's constant pressure eventually paid off.
Wayne Rooney, on as a substitute, crossed for Radzinski to head home after 85 minutes and then, in injury time, the Canadian thundered an angled shot into the roof of the net.
The match began as a tight and hard-fought contest with two disciplined teams denying the other time or space on the ball.
33 mins: Beattie puts Southampton ahead
85: Radzinski levels for Everton
92: Radzinski powers in the winner
Everton had the better of the early exchanges but Southampton's defence held firm.
The pace of Radzinski saw him break down the inside right for Everton only for his cross to find a Saints defender instead of three team-mates waiting for a ball.
Steve Watson had two well-struck efforts blocked before the home side were caught by a Saints sucker-punch.
Just minutes after Everton escaped when they were two against three, a first-time ball over the top of the Everton defence seeing Beattie beat the offside trap and score.
Everton keeper Richard Wright got a touch to the striker's chip but could not stop it going in.
Beattie's 17th of the season was in vain
As the second half got underway, with Everton pushing for an equaliser, Radzinski dispossessed Saints defender Michael Svensson and should have done better than putting an attempted chip into the grateful arms of Antti Niemi.
Niemi also palmed a Gary Naysmith shot over his crossbar as the game opened up into an exciting affair.
Beattie's far post volley was impressively saved by keeper Wright before Radzinski hit the post at the other end.
Southampton's goal lived a charmed life with keeper Niemi making the most of his fortune.
But the visitors' luck ran out after 85 minutes when Radzinski headed home his first goal.
And Everton might have had a winner through Kevin Campbell only for the ball to unwittingly strike Niemi before evading Rooney's touch at the far post.
But Radzinski struck in stoppage time to give David Moyes' team a vital three points in their Champions League quest.
Everton: Wright, Pistone, Weir, Stubbs, Unsworth, Watson,
Li Tie (Gravesen 59), Gemmill, Naysmith (Rooney 64),
McBride (Campbell 59), Radzinski.
Subs Not Used: Yobo, Gerrard.
Southampton: Niemi, Telfer, Michael Svensson, Lundekvam,
Higginbotham, Fernandes (Dodd 70), Anders Svensson (Davies 88),
Oakley, Prutton, Beattie, Ormerod (Tessem 61).
Subs Not Used: Jones, Williams.
Referee: D Elleray (Middlesex).