The home fans were crying out for a penalty after just seven minutes, alleging that Yves Bissouma had blocked Mohammed Kudus’ cross with his arm. That was waved away, and just before the quarter-hour mark, Spurs drew first blood.
Djed Spence sent a hopeful long ball for Mathys Tel to chase, and the Frenchman didn’t give up on it and forced Max Kilman into an error.
Tel composed himself to play a pass across the middle to countryman Wilson Odobert, who had time to take a touch from six yards before rolling into the net for his first league goal in Tottenham colours.
The Hammers responded well, and another claim of a rogue Tottenham hand fell on deaf ears with Ben Davies the relieved party this time.
However, less than 15 minutes after falling behind, captain Jarrod Bowen drew his side level from a narrow angle after being played in by a perfectly-weighted Aaron Wan-Bissaka pass.
Richarlison had the best of the opportunities to give the visitors a HT lead, but first steered Spence’s ball over the top before his cross-shot drifted across the face of goal.
The first real chance after the restart fell the way of the hosts as Kudus picked out Bowen at the back post, but his dipping volley just flashed wide of Guglielmo Vicario’s far post.
Kudus caused trouble for Tottenham throughout, and on 70 minutes his whipped cross connected with the airborne Niclas Füllkrug, but the German couldn’t keep his header down.
Tottenham are still without Son Heung-min, while James Maddison and Dominic Solanke weren’t risked after picking up knocks in Thursday’s UEFA Europa League semi-final.
Ange Postecoglou’s side could have done with them given their struggles to create anything of note in the second half here.
Pape Matar Sarr’s vicious effort from range that whistled over the top was as close as they came to a winner in another insipid domestic display.
Bowen came close again with less than 10 minutes remaining with a diving near-post header, which Vicario had to react quickly to parry away.
Ultimately, West Ham were shut out which denied them a first victory since February, although it marked a fifth successive home H2H without defeat.
They remain 17th, a point and a place behind Spurs, whose focus remains trained on their European duties this week.
Flashscore Man of the Match: Djed Spence (Tottenham Hotspur)