McInnes was in charge of Rangers for the first time since arriving from Hearts in the close season.
The former Rangers midfielder watched as Lachlan Rose put United ahead in the first half at Tannadice.
Thelo Aasgaard equalised after the interval to spare the title contenders from an embarrassing start to the campaign.
Just 76 days after Celtic pipped Hearts to the Scottish title in a pulsating finish to an incredible season, Rangers made a spluttering start to their bid to dethrone their bitter rivals.
McInnes gave debuts to Lawrence Shankland and Cammy Devlin, who followed him to Rangers from Hearts, while fellow new signings Ivor Pandur and Ben Godfrey also made their first appearances.
But Rangers' new boys struggled to make their presence felt in a disjointed first-half display.
Instead, it was one of United's close-season recruits who broke the deadlock in the 38th minute.
Rangers were guilty of sloppy defending as Jesse Randall was allowed to send in a low cross that wasn't cleared before Australian striker Rose prodded home from close range.
McInnes responded to United scoring from their first shot on target by sending on Youssef Chermiti and debutant Dan Neil for the second half.
Rangers were significantly improved by the changes and Aasgaard hauled them level in the 56th minute, drilling past United keeper Jack Walton from 12 yards after Shankland's muscular challenge unsettled the hosts.
It was hardly the start McInnes was hoping for, underling the size of the task facing him to finally get his hands on the Scottish title.
Heartbroken
In the aftermath of Rangers' second successive trophyless season, Danny Rohl was allowed to leave for Red Bull Salzburg, paving the way for boyhood fan McInnes to play the role of the prodigal son.
The 55-year-old has been tasked with bringing Rangers their first title since Steven Gerrard led them to the trophy in 2021.
That was the only time in the last 15 seasons that Celtic failed to win the title and McInnes has to prove he can bounce back from the devastation of Hearts' agonising near-miss last term.
Hearts were on the brink of ending the Old Firm's four-decade dominance of the Scottish title when they took the lead against Celtic on the final day of the season.
But a late collapse gifted yet another title to Celtic, leaving them heartbroken and destined for a turbulent summer after blowing a golden opportunity to win their first Scottish crown since 1960.
McInnes departed for Ibrox, with his Hearts successor Wouter Vrancken presiding over a dismal Champions League qualifying round exit against Sturm Graz earlier in July.
It is an ominous introduction for the Belgian, who starts Hearts' domestic campaign at Aberdeen on Saturday.
Celtic's domestic double under interim boss Martin O'Neill last season convinced the club to retain the 74-year-old on a permanent deal.
Yet, despite a fifth successive title, there is still unrest among supporters frustrated with the direction of the club.
The Celtic board's parsimonious approach to the transfer market is the main bone of contention ahead of their opener at home to Dundee on Monday.
Signing Camilo Duran and Kasper Hogh may not be enough to stop supporters from rebelling after popular Japan forward Daizen Maeda joined Ipswich.
