Everton 1 Arsenal 0: Andrew Johnson grabbed a late winner as snow fell on Goodison Park to add further woe to Arsenal's season.
Beaten in three cup competitions of late, they failed to take advantage of Liverpool's dropped points earlier in the day when their rivals for third spot could only draw at Aston Villa.
Arsenal slipped up again, and so did Wenger, falling over on the touch-line in the snow as he tried to encourage his side to cope with Everton's late surge.
And Johnson struck his 12th goal of the season in the first minute of injury time to send Everton back into sixth spot in their own quest for European qualification.
In the week that boss David Moyes celebrated his fifth year in charge of the club, this was another famous scalp for the Scot to relish.
A minute into injury-time, Everton grabbed the lead. Mikel Arteta's corner was nodded on by Johnson, Arsenal failed to clear and the ball came back to the striker to drill home from 12 yards with his left foot.
Anichebe, who had been heavily involved in the penalty-box battle that led to the goal, found himself booked before the restart.