Albion looked set for three precious points in their battle to stay in the Premier League when Matej Vydra and Chris Brunt struck in the first four minutes and a third goal from Stephane Sessegnon put them firmly in command just 31 minutes in at The Hawthorns.
Emmanuel Adebayor had a penalty saved by West Brom goalkeeper Ben Foster before Sessegnon struck, but Jonas Olsson's own-goal before half time gave Tottenham hope and then Harry Kane's 70th-minute strike set up a tense finale.
Albion let an early 2-0 lead slip against Cardiff City in their last home game and had to settle for a point after conceding a stoppage-time equaliser to draw 3-3, so there must have been a sense of deja vu for coach Mel when Christian Eriksen denied them once again in time added on.
Just like his opposite number Tim Sherwood, Mel is facing end-of-season talks over his future and Saturday's capitulation did little to ease the pressure on the Spaniard, who cut a frustated figure after West Brom's latest capitulation.
He said: "We started really well and had a very good first half, but the result has gone against us again. The players are down but we have five big games left.
"The problem is we're so keen to win the points to stay up. We need to play the same way regardless of whether we're 0-0 or 3-0 ahead.
"It's another point and we did some things very well but it feels like two points dropped.
"We are cross as we needed the points. (We) got tired. I didn't tell the players to drop back, Tottenham played well.
"Now we need a reaction like we had at Norwich (when West Brom won 1-0)."
Albion are now just three points above third-bottom Fulham, albeit with a game in hand, after the London club beat fellow strugglers Norwich City. Second-bottom Cardiff also secured a much-needed victory at Southampton on Saturday.
Mel's side face a daunting trip to title-chasing Manchester City in their next Premier League fixture on April 21.
