Gylfi Sigurdsson then struck the crossbar as we looked in control with time running out.
But it all changed as the clock reached 90 minutes.
Steven Pienaar levelled with a powerful header and 90 seconds later – in the 92nd minute – Nikica Jelavic pounced on substitute Apostolos Vellios’ overhead kick to snatch victory.
“It’s difficult to take,” said Andre at Goodison. “We can say that in the first half, we didn’t play well but in the second half we improved a lot and bounced back.
“The last minutes were our best with Clint’s goal and Gylfi’s chance, we kept the ball and played well, but then the game changed completely against the run of play.
“To be fair, Everton had a first half where they could have scored, that’s the reality.
"But we managed hold on to that 0-0, then had a brilliant second half and to see it escape from us in the last minutes is difficult to take.”
The result leaves us in fifth place, level on points with Everton in fourth and West Brom in sixth.
Clint Dempsey’s strike in the 76th minute looked set to secure a fourth-successive victory the Premier League and inflict Everton’s first home defeat this term.