Manchester United are on six points – their poorest start since 1986 – and Tottenham have three less and remain stuck in the relegation zone: testing times for Michael Carrick and Roberto De Zerbi, who must somehow revive their teams following a contest that was lit up by a moment of quality in the 73rd minute.

Matheus Cunha was fed by Luke Shaw down the left and the Brazilian crossed to Bryan Mbeumo, who spun and finished for United. It drew delirious chants of "You're going down with the City": Spurs, at this stage, were rock-bottom, and Manchester City's long-term future in the division is in the balance.

Darker scenes followed when Shaw chased Bruno Fernandes's ball and Rodrigo Bentancur launched a scissor challenge that, if it had connected with the left-back, might have caused serious injury.

An incensed Shaw, surely reminded of his horrific double-leg break sustained 11 years ago at PSV Eindhoven, hared after Bentancur and shoved him over. Up came the midfielder to push his head into Shaw's, who went down as a melee involving both benches ensued.

Stuart Attwell sent Bentancur off and issued yellow cards to Shaw – lucky to escape a red, too, for the push – and Jan Paul van Hecke.

All of this followed a near snoozefest in which Spurs could not finish and United were disjointed: the tale, in microcosm, of their seasons.

There was more, though, as Tottenham scored an added-time equaliser, only their third league goal. Senne Lammens and Lisandro Martínez were United's culprits as Sandro Tonali's floated cross from the left should have been cleared by the Argentinian, but instead Dominic Solanke outfought him and headed past United's goalkeeper, who watched the ball go in.

While averting a fourth defeat, Spurs still remain winless after their opening six league games, for only the fourth time in their history. The draw, too, means there is no clear answer to the pre-game question of which manager is under more pressure, as both De Zerbi and Carrick remain in need of a victory – or three.

When the Italian scans the table, he sees his beleaguered side third bottom, while United remain in 12th and with a solitary victory claimed all season, against Ipswich.

De Zerbi now takes his squad to Marbella for warm-weather training, while Carrick's men are at Atlético Madrid on Tuesday in the Champions League.

After volleys of "You cheating bastards – you know what you are" rang out from both sets of fans (directed at City, again) Lammens went close to a nightmare start. A loose pass out was nabbed by Lucas Bergvall and the ball rolled to Solanke. Yet, as is Spurs' prevailing problem, the centre-forward failed to finish, the shot saved by a relieved Lammens.

United's goalkeeper was jittery again, when Martínez tapped the ball to him on his goalline and he dawdled before hoofing clear.

The reports said De Zerbi's men had performed well, at times, but could not finish: a certifiable hindrance in this sport.

No boon, too, for any team is hesitation, as when Youri Tielemans waited for the ball to bounce, Tottenham pounced, and suddenly Sávio was heading forward. A sliding challenge from Leny Yoro, picked at right-back, saved a scattered rearguard.

This pointed to a Spurs ascendancy that was a headscratcher for Carrick and yet more profligacy from their visitors saved United when Mohammed Kudus's cross found Archie Gray and the young right-back beat Lammens but not his right post.

Carrick wants his team to have control of contests but there was close to zero throughout, though on the hour Carlos Baleba came on for his debut and immediately spun and flicked the ball deftly into Fernandes' path, and you were reminded what skill can do.

Now came the breathless denouement – a point, at the close, feeling fair, though unsatisfactory for both sides, who need to kickstart their campaign.

De Zerbi will aim to do so in Spain. "We are a great group of players but we are not a team yet and to be a team is to play for the teammates – suffer together, attack together," he said.