Set-piece specialist Christian Eriksen, whose double against Sheffield United led Spurs to the Capital One Cup final in midweek, opened the scoring with a free-kick on six minutes.
Harry Kane then powered home a second 10 minutes later as Spurs struck twice in the opening quarter of an hour to stun Tony Pulis’ side.
The Baggies rallied and had several chances to haul themselves back into the game but efforts from James Morrison and Claudio Yacob drew fine saves from the inspired Hugo Lloris, while Craig Dawson, having beaten the keeper, saw his header cannon off the bar.
Having ended a four-game wait for a goal with his first, Kane notched his second just after the hour, converting from the penalty spot for his 20th of the season after referee Kevin Friend adjudged Joleon Lescott to have handled Kyle Walker’s cross in the box.
The third goal all-but secured victory for the visitors as Spurs afforded Albion a number of chances in the closing stages without completely relinquishing their grip on the game.
The trip to The Hawthorns was Spurs’ ninth game in a congested January fixture list and, prior to the game, Mauricio Pochettino expressed his concerns over the fitness of his players.
Seemingly buoyed from booking their place at Wembley, his side showed no sign of fatigue as they raced into an early lead.
Outnumbering their opponents in midfield, Spurs dominated the opening exchanges and were soon a goal up as Eriksen curled a free-kick over the wall and out of the reach of Ben Foster.
Ten minutes later, it was two as Kane rounded off a fine Spurs attack, collecting Mousa Dembele’s ball, cutting inside Andre Wisdom and rifling home from just inside the area.
Albion then began to grow into the game and had two chances in quick succession to reduce the deficit.
Morrison created a shooting opportunity at the edge of the area and appeared to have found the top left-hand corner of Lloris’ goal, only for the Frenchman produce an exquisite save to deny the Scot.
And the Spurs captain was at it again a minute later, palming Yacob’s effort away from goal following a superb training ground set-piece which involved Morrison, Chris Brunt and Saido Berahino.
Dawson’s towering header rattled the frame of Tottenham’s goal before the break as Albion pushed for a lifeline which failed to materialise.
Spurs started the second half as they had the first, racing out of the blocks as Eriksen’s turn outside the box and left-footed drive came close to making it three.
However, the third was not far away as Kane struck from the spot after Lescott’s handball.
Berahino and strike partner Victor Anichebe continued to test Lloris, as too did substitute Craig Gardner, but his effort woud not have counted after he was penalised for handball.
Kane’s hopes of a hat-trick were dashed as Roberto Soldado replaced him with minutes remaining but the result was in hand for League Cup finalists.
Spurs leapfrog north London rivals Arsenal, who they play next weekend, into fifth while the defeat for Albion, their first under Pulis, sees them drop a place to 15th.
Soccer Saturday reaction – Phil Thompson
Spurs were the better team and you can’t take anything away from them. They were absolutely out of the blocks. You’d think there’d be a few tired legs after midweek – nothing of the sort. Kane comes back in there, the link-up between Kane and Eriksen is just absolutely marvellous. This was a team at ease with itself in the first 20 minutes, and West Brom are thinking, ‘How do we get out of our own half?’”
“Should Kane be in the England squad?: “Absolutely. If he’s not in that squad… I think this guy is so close to a start it’s untrue. He doesn’t often give it away. It looks as though he’s falling into people, but he’s in complete control of it. If you’re a defender trying to get close to him, it’s extremely difficult. I would have him in, I’d give him a start, he deserves it. He scored his 20th goal of the season – he should be in.”
West Brom: Foster (6), Wisdom (5), McAuley (6), Dawson (6), Lescott (5), McManaman (6), Yacob (6), Morrison (7), brunt (6), Anichebe (7), Berahino (7).
Used subs: Gardner (5), Ideye (4).
Tottenham: Lloris (8), Walker (7), Fazio (6), Vertonghen (6), Rose (7), Paulinho (7), Mason (6), Lamela (6), Dembele (7), Eriksen (8), Kane (9).
Used subs: Chadli (5), Stambouli (5), Soldado (4).
Man of the Match: Harry Kane.