Danny Simpson, Jonny Evans and Gerard Pique were all drafted into defence, while the likes of Chris Eagles, Darren Fletcher and Louis Saha all earned rare starts.
Victory for United would have made them the first English side - and only the fourth team in Champions League history - to win all six of their group stage matches.
However, despite taking the lead through Pique in the first half, the visitors were slowly pegged back and Mancini's strike midway through the second period earned the Italians a deserved share of the spoils.
United started in confident mood and Alexander Doni has to be alert to tip over a header from John O'Shea following a chipped cross from the right by Fletcher.
In a rare attack at the other end, Mauro Esposito should have done better when glancing Cicinho's cross on the half-hour wide of the far post.
United responded and took the lead after 34 minutes through Spanish defender Pique.
Nani delivered a quality corner from the left and Pique ran off his marker before heading home from eight yards with relative ease.
Mancini came within a whisker of firing Roma level on 38 minuets when he picked up Francesco Totti's square pass from the penalty spot but drilled a close-range effort against the crossbar.
Esposito also failed to convert the follow up under pressure from O'Shea at the back post.
Tomasz Kuszczak then denied Mancini at full stretch as he dived to his right to repel a first-time effort from the Brazilian after a swift break down the United right had threatened to bring about the equaliser.
After the interval, United kept up the pressure with captain for the night Wayne Rooney involved in all their best moves.
In the 55th minute Doni tipped the ball over his own crossbar after Michael Carrick had diverted Nani's near-post corner goalwards and a melee ensued.
The Roma keeper then kept his side in the game when he charged off his line to beat away a Saha effort after a one-two with Rooney had cut the home defence wide open.
But when Rooney was replaced midway through the second half, Roma visibly grew in confidence and they were level in the 71st minute.
Mirko Vucinic spotted Mancini in acres of space on the edge of the box and the tricky winger cut inside Wes Brown before picking his spot beyond the keeper with a composed piece of finishing.
There was still time for Vucinic to rattle the foot of the post and blaze a stoppage-time chance over the bar as United held on at the end for a deserved point.