Spurs toiled away with little reward for much of the match, but Harry Kane ensured that they would not end up empty-handed with a second-half equaliser which was enough to earn his side a point.
The Baggies went into the match off the back of four straight defeats and without a win in 11 across all competitions, but it took less than four minutes for them to stun Wembley into silence with a shock early opener.
Some sloppy play from Dele Alli in midfield allowed Jake Livermore to win possession and slide a ball through for Rondon, who shrugged off the challenge from Davinson Sanchez before seeing his scuffed finish wrong-foot Hugo Lloris and trickle into the bottom corner.
Spurs quickly took control of possession, but West Brom's disciplined organisation bore all the hallmarks of a Pulis side as they limited the hosts to only a Kane half-chance in the opening 25 minutes.
It wasn't until shortly before the half-hour mark that Tottenham truly threatened the West Brom goal for the first time, with Kane spinning away from Ahmed Hegazi before firing a tame low strike narrowly past the post.
Ben Foster was then called into action for the first time five minutes later, scooping away an awkward strike from Son Heung-min after the South Korean attacker had cut inside from the left flank to create space to shoot.
The resulting corner was only cleared as far as Christian Eriksen, but the Dane's dipping half-volley flew comfortably off target as West Brom continued to limit Spurs to long-range efforts.
Indeed, the hosts' first shot from inside the box of any real note did not arrive until four minutes before half time when Eric Dier rose highest to meet Kieran Trippier's corner, but his header was plucked out of the air by Foster.
Arguably Tottenham's best attacking moment of the half came through Son, who beat Matt Phillips down the left channel before fizzing a low ball across the six-yard box which was begging for a touch that never arrived.
Son came close once more before the interval when he saw a dipping strike deflect onto the roof of the net, but a frustrated Spurs were forced to go into half time trailing despite dominating the possession.
The hosts quickly picked up where they left off in the second half too, but once again they struggled to create clear chances against a disciplined defensive outfit.
Indeed, it was West Brom who came closest to adding the game's second goal before the hour mark as Phillips cut inside before arrowing a low strike just wide of the far post on a rare foray forward.
Spurs did come close to an equaliser with a little over 20 minutes remaining when a corner was only cleared as far as Trippier, but his scuffed volley bounced across goal and Alli was inches short of getting a touch to it.
The hosts did finally level things up in the 74th minute, though, as Alli fed a low ball into the near post which Kane diverted past Foster for his ninth league goal of the campaign, drawing him level with Mohamed Salah as the division's top scorer.
Kane had been kept quiet for much of the afternoon up until that point, but he suddenly looked in the mood and came close again when he rose highest inside the box to divert a Trippier cross off target.
The England international then saw a deflected effort spilled by Foster, who recovered to collect it at the second attempt, before curling a low strike narrowly wide of the far post after turning Hegazi just outside the area.
It looked at that stage as though Spurs might go on to win the game, but it was West Brom who came closest to stealing all three points in five minutes of stoppage time as first Hal Robson-Kanu drilled a powerful effort straight at Lloris before Rondon failed to get enough on his finish having been picked out inside the area.
Neither side could find a winner in the closing stages, though, as Tottenham dropped two more points in their title challenge to ensure that Manchester City could climb 13 points clear of them with victory over Huddersfield Town on Sunday.
Spurs have now won just one of their last four Premier League games, whereas West Brom are now one point clear of the relegation having ended their four-match losing streak - although they remaining without a win since August.
Tottenham Hotspur (3-5-2): Lloris; Trippier, Sanchez, Vertonghen (Llorente, 60'), Davies; Dier, Winks (Dembele, 61'); Son, Eriksen, Dele; Kane
West Bromwich Albion (4-4-2): Foster; Nyom, Evans, Hegazi, Gibbs; Livermore, Barry (Barry, 79'); Field (McClean, 67'), Phillips; Rodriguez (Robson-Kanu, 67'), Rondon