It was another impressive performance from Tony Pulis' Baggies who never lay down despite being under pressure for the majority of the encounter.
The Foxes found themselves behind in the 11th minute when Salomon Rondon helped himself to his second goal in his past two away appearances when he got on the end of a lovely ball from Darren fletcher, before outmuscling Robert Huth, and finishing neatly beyond Kasper Schmeichel.
A goal for Claudio Ranieri's men was definitely coming and it occurred on the half-hour mark when Danny Drinkwater's long range effort took a massive piece of Jonas Olsson on the way through before looping wickedly over a hapless Ben Foster.
Seven minutes later, Jamie Vardy was so unlucky to see his header crash into the crossbar but Leicester edged in front on the stroke of half-time when Andy King, in for the injured N'Golo Kante, slotted home Riyad Mahrez's delightful knockdown.
The joy was short-lived, however, as Craig Gardner stepped up to fire a superb free-kick into Schmeichel's top right corner in the 50th minute marking two scoring outings in a row for him.
Leicester desperately chased a winner as they attempted to stretch their lead over Tottenham Hotspur to five points but were unable to breach Foster's goal despite the best efforts of Shinji Okazaki, Vardy and Wes Morgan who were denied by both the crossbar and the Baggies keeper.
The draw leaves the Foxes just three points clear of Spurs who can replace them at the summit they win at West Ham United on Wednesday while Albion remained 13th thanks to a third straight game without defeat.
2015/16 Barclays Premier League - season scores