The surprise slip-up by Spurs came courtesy of a pair of goals from Baggies defender Craig Dawson who scored an own-goal in the first half before producing an equaliser at the same end with just over 15 minutes remaining.
Earlier in the contest, Albion keeper Boaz Myhill came up with a brilliant save to turn Harry Kane's angled effort onto the woodwork before Christian Eriksen's free-kick skimmed the top of the crossbar.
Myhill was soon at it again to deny a fierce Kane effort before Spurs took the lead inside 33 minutes when Eriksen's set-piece ball, destined for Jan Vertonghen, squirmed its way under the visiting gloveman off the head and shoulder of Dawson.
Tottenham were again unlucky just before the hour-mark when Eriksen fed Erik Lamela who put his attempt into the base of the upright but Dawson was able to make amends for his earlier blunder by rising above Eric Dier to nod home Craig Gardner's corner in the 73rd minute.
At the final whistle, some Spurs slumped to the turf knowing that they had missed a golden opportunity to keep the pressure on Leicester who will now lift the premiership trophy in Manchester on the weekend if they are able to overcome the Red Devils.
2015/16 Barclays Premier League - season scores