Sam Burns' strike ensured Rovers picked up a point in their first game of 2021, but Billy Barr's charges probably deserved all three against Manchester City's Under-23s.
Burns tucked home from close range in the first half to deservedly put the visitors in front at City's academy stadium.
However, an error from Louie Annesley let in James McAtee, whose effort was saved before Ben Knight put in the rebound.
Rovers almost got an instant response, but Ben Paton's strike hit the post just a few minutes later.
Annesley's evening then went from bad to worse late on, with the defender shown a straight red card for a collision with Knight with only seven minutes remaining.
A point was the least Rovers deserved, and another positive was Elliott Bennett coming through 45 minutes unscathed in Manchester.
The big team news was the return of Bennett, who was back on the pitch for the first time since picking up an ankle injury in training three months ago.
The 32-year-old came in to partner Isaac Whitehall in central midfield, whilst Tyrhys Dolan also started, lining up on the right against the club where he first began his career.
For City, Liam Delap sat out through suspension, but they did include the likes of Cole Palmer, McAtee and Knight in their starting XI, who all featured against Rovers' Under-18s in the semi-finals of the FA Youth Cup back in November.
It was the returning Bennett who had the first shot in anger, but his strike was well held by James Trafford, who was actually sent off against Rovers when the two sides met on the opening day of the season.
Bennett was continuing to have an influence, and it was his slick pass that began the move for the opening goal of the game soon after.
His pick out was perfect for Dan Pike to collect on the right, and once Dolan offered support on the overlap, the winger's low cross was spot on to allow Burns to slot home first time from close range.
It was almost 2-0 just moments later, but Whitehall curled just past Trafford's left-hand post after more good work from Dolan worked an opening.
A fine reaction stop from Eastham then denied City an equaliser in the hosts' first foray forward, before Callum Doyle slammed over on the stretch as the game began to open up.
Rovers looked to be in control of the first half, and Burns' strike ensured that Rovers deservedly went into the break ahead in Manchester.
Both sides made a change at the break, with Bennett getting a good half under his belt to allow Joe Nolan to appear for the second 45 minutes just a few days after penning a deal with the club after impressing on trial.
Rovers kept up the intensity after the break, with the impressive Dolan cutting in from the right flank before seeing his low attempt stopped by Trafford as the game quickly approached the hour mark.
The battle between Dolan and Trafford continued, with the City 'keeper diving down low to his right to tip away the Rovers man's drive from range.
That was to prove vital, with the hosts finding an equalising goal in the next move of the match.
A lapse in concentration from Annesley saw the big defender robbed by McAtee, and although Eastham did brilliantly to save, the ball broke kindly to Knight who slotted home the rebound.
That was harsh on Rovers, who had produced an excellent display throughout the contest up until that point.
Rovers went in search of a response, but Paton's strike agonisingly crashed against the outside of the post just three minutes later.
It wasn't going to be Annesley's night, and having made the mistake for the City equaliser, the Gibraltar international was then shown a straight red card after colliding with Knight outside the box when the playmaker went through on goal.
Rovers were forced to dig in to see the game out, but were relatively comfortable for the final minutes as Barr's boys begin 2021 with a point on the road.
Manchester City Under-23s: Trafford, Egan-Riley (c), Burns, Gomes, Doyle, Lavia (Tarensi Cordon, 86), Edozie (Diounhou, 75), Palmer, McAtee, Knight, Nmecha (Robertson, 46).
Unused substitutes: Moulden, Hodge.
Goal: Knight, 69.
Booked: Lavia, 77.
Rovers Under-23s: Eastham, Pike, Thompson, Bennett (c) (Nolan, 46), Barnes, Annesley, Dolan, Whitehall, Vale, Paton, Burns.
Unused substitutes: Stergiakis, Durrant, McBride, Brennan.
Goal: Burns, 17.
Booked: Vale, 35, Pike, 66.
Sent off: Annesley, 82
Referee: Martin Woods.