But, in a breathless conclusion to another lively Dundee derby, the visitors scored two goals in the closing stages to draw level after a quick-fire Blair Spittal double for United.
Auxiliary striker James McPake’s equaliser arrived in the last seconds of four minutes of time added on.
Paul Hartley’s side were again guilty of wasting several chances although, as on Saturday, when Hearts’ Neil Alexander distinguished himself, the Dens Park side encountered a goalkeeper in inspired form.
Luis Zwick, making his debut in a Dundee derby, excelled in the way others have not in recent times.
The 21 year-old made some crucial stops for his side in the opening half but suffered a heart-breaking spill at the end, which allowed McPake to slide in and convert the last chance for which Dundee had yearned.
Hartley was sent to the stand for leaving his technical area amid the wild celebrations and the game barely had time to kick off again.
Zwick had enjoyed a far quieter second half before being beaten by the latest stunning strike by Greg Stewart with eight minutes of normal time left, as Dundee mounted a comeback that earned them a very satisfactory point from an evening that had begun to go very wrong indeed. It was all set to be teenager Blair Spittal’s night.
He might have scored a second-half hat-trick as United, having drawn the sting from Dundee, aimed to make the most of their home advantage, scoring twice through the 19-year-old midfielder in the space of three second-half minutes.
With Rory Loy restored to the starting line-up in place of Paul McGowan, Dundee seemed to be paying little heed to the multi-goal defeats in the league here last season.
Hartley opted for an adventurous line-up; Stewart was handed licence to roam behind a front two of Loy and Kane Hemmings.
Until Thomas Konrad came on to replace Julen Extabeguren, who received a cut head in an early clash with Darko Bodul, only James McPake – another early cut victim, though he stayed on – and Stewart were in the side defeated 6-2 by United on New Year’s Day.
Perhaps for this reason, that thrashing, as well as the 3-0 reversal here on the last day of the season, did not seem to be preying on their minds. There was little evidence of trepidation from the away side, who took the game to their hosts almost immediately from kick-off.
Their best chance of the half fell to Ross after only ten minutes. Paul McGinn’s cross-cum-shot was beaten out by Zwick. Nick Ross’s first effort was well blocked by the keeper – though Ross knows he should have made a better fist of converting the chance.
He was given the sniff of a second chance but Zwick bravely smothered the loose ball, and then accused Ross of making a dangerous challenge. But play raged on, most of it occurring in the United half of the field.
Unusually given their derby record of late, United were finding it hard to gain a foothold in the game. A Rankin shot from long distance and a Scott Fraser free-kick from a good position that was headed over his own bar by Ross were the best they could muster.
Nevertheless, given their torrid experiences last season, Dundee were probably just as content to reach half-time with the score goalless.
By the same stage on the first day of the year, they were 4-1 down. But they very nearly did go behind shortly after the re-start. Dundee had already suffered a severe blow before Rankin’s strong effort was well saved low to his left by Bain.
The sight of Kevin Thomson leaving the pitch before the end of the 90 minutes is not a new one but it had to be treated as a setback for Dundee since it occurred only a few minutes into the second half. McGowan replaced the skipper.
However, it was the arrival of Simon Murray, a boyhood Dundee fan, and Chris Erskine that threatened to have the greatest impact on the game.
The home side seemed immediately re-energised. Within another seven minutes, they were two goals up, and though neither Murray nor Erskine scored, the switch to two up front suddenly unsettled Dundee’s reorganised defence.
But it was Spittal, on from the start and a thorn in Dundee’s side last season as well, who made the difference.
His first goal, after 64 minutes, was an exquisite finish. Taking a lay-off from Rankin in his stride, he sidestepped McPake and then thrashed an unstoppable shot past Bain.
If that was bad enough for the visitors, it quickly got worse. Again Spittal was the one to drive a spear into Dundee after a lightning-quick break in which Erskine slid a perfect ball into the midfielder’s path. Spittal, his confidence up, took the chance first-time, sweeping the ball past Bain from an angle.
Spittal had chances to secure a memorable derby hat-trick but was denied by Bain from a free-kick before driving another effort just past.
Dundee livened up again towards the end, with Stewart scoring with a sweet left-footed strike into the top corner after combining with McGowan. But was it again too little, too late?
United almost secured the points through Murray, whose shot was tipped on to the bar in breathtaking fashion by Bain. It meant everything to Dundee in the end as McPake slid in to salvage a draw after Gary Harkins’ long-distance shot was only parried by Zwick, whose performance had been faultless otherwise.
Dundee Utd: Zwick, McGowan, Durnan, Donaldson, Dixon, Souttar, Rankin, Connolly (Murray 60), Fraser (Erskine 60), Spittal, Bodul (Telfer 71). Subs not used: Dillon, Muirhead, McCallum, Lochhead.
Dundee: Bain, McGinn, McPake, Etxabeguren (Konrad 9), Holt, Harkins, Thomson (McGowan 50), Ross, Stewart, Loy, Hemmings (Low 71). Subs not used: Irvine, Meggatt, Ferry, Mitchell.