It was another under-par performance from the hosts at the Tottenham Hotspur Stadium, although they took the lead in the second half through Son Heung-min's third goal of the week.
A 78th-minute George Baldock leveller was enough for the Blades to come away with a deserved point, though, and it could have been even better for Chris Wilder's men had they not seen a goal controversially ruled out by VAR.
The result takes Sheffield United up to fifth in the table after 12 games of the season, while Spurs drop down to 12th with only 14 points so far this term.
The visitors arrived in North London sitting five places above their hosts and having lost just one away league game all calendar year - the joint-lowest alongside Liverpool in the top four divisions of English football - so it was perhaps not a surprise to see them make the brighter start to the match.
Stand-in Spurs keeper Paulo Gazzaniga was called into action twice inside the opening 10 minutes, first tipping Oliver Norwood's early deflected drive over the top and then getting down well to make a more routine save from John Fleck's rasping low strike.
Tottenham did begin to grow into the game, though, and should have taken the lead after 15 minutes when Harry Kane darted in front of his marker to meet Serge Aurier's low cross, only to fluff his lines with the finish and skew a golden opportunity wide.
Giovani Lo Celso - making his first Premier League start for the hosts - and Son both also fired off target as they failed to test Dean Henderson during the first half, with Gazzaniga the busier of the two keepers and making another routine save to gather David McGoldrick's low shot midway through the half.
It was Lundstram, who scored twice in the 3-0 win over Burnley last weekend, who looked most like netting again for Sheffield United throughout the opening 45 minutes, and he should have done better shortly before the half-hour mark when he nudged a cross narrowly wide of the far post.
Lundstram came even closer to grabbing the opener moments later when he crashed a powerful curling effort against the upright after being teed up by Jack O'Connell inside the area.
A 30-yard effort from Aurier which fizzed off target summed up Tottenham's growing frustration as they failed to turn their 65% first-half possession into meaningful chances, although they did come close to an opener seven minutes before the interval when Lo Celso slid a shot just wide from Son's cutback.
It was the first time Spurs had failed to register a shot on target in the first half of a home league game since January - and the first time ever at their new stadium - and Mauricio Pochettino was also forced into a half-time change as Harry Winks replaced Tanguy Ndombele.
Sheffield United again made an encouraging start to the half, though, and they almost took the lead through the in-form Lys Mousset seven minutes after the restart when he dribbled into the box before spinning away from Davinson Sanchez and drilling an effort inches wide.
Tottenham's first shot on target finally arrived just two minutes after that as Son latched on to Dele Alli's through-ball and drew a save from Henderson, and it was the South Korean who broke the deadlock shortly afterwards to make it five goals in his last five games for the club.
The attacker, who was only able to feature after seeing his red card against Everton overturned, benefited from some good fortune as the ball bounced off Enda Stevens and into his path inside the area, allowing him to smuggle a tame shot through the legs of Henderson, who should have done better.
The Tottenham celebrations were initially short-lived as Sheffield United had the ball in the back of the net at the other end just two minutes later, with McGoldrick tapping home from close range at the back post.
However, a VAR check of almost four minutes eventually ruled that Lundstram's big toe had strayed beyond the last man, cancelling the goal by the slimmest of margins.
There was a less controversial use of the video assistant when Son went down inside the box while skewing a shot wide under pressure, with Tottenham's penalty appeals quickly turned down.
The Blades more than held their own throughout the contest, though, and they were well worth their equaliser when it arrived 12 minutes from time as Baldock's cross\shot nestled into the far corner via the slightest touch off Eric Dier's header.
Another VAR check had the visiting fans feeling a familiar sense of dread, but this time the goal correctly stood and Spurs were left facing yet more dropped points in an underwhelming Premier League campaign.
The hosts were aided by six minutes of added-on time too, but it was only a powerful drive from Lucas Moura midway through that additional time that threatened the United goal as Wilder's outfit held on for another impressive result.
Spurs have now dropped a league-high 12 points from winning positions this season and have only kept one clean sheet all season, leaving them now only three points clear of 17th-placed Aston Villa.
TOTTENHAM (4-2-3-1): Gazzaniga; Aurier (Lucas 86'), Sanchez, Dier, Davies; Sissoko, Ndombele (Winks 46'); Lo Celso, Alli (Foyth 72'), Son; Kane
SHEFFIELD UNITED (3-5-2): Henderson; Basham, Egan, O'Connell; Baldock, Lundstram, Norwood, Fleck, Stevens; Mousset (Robinson 87'), McGoldrick (Freeman 95')