A much-changed Manchester United side earned a draw against Italian giants Roma to protect their unbeaten record in the Champions League this season.
Pique celebrates his second goal in two Champions League games
A disappointing first-half livened up when Gerard Pique stole in at the near post to head United in front.
Mancini clipped a shot on to the bar as Roma fought back, before Louis Saha was denied by a fine save from Doni.
Mancini slammed in a leveller from substitute Mirko Vucinic's pass, before the Montenegran struck the woodwork.
Mancini's goal meant United do not become only the fifth team to establish a perfect record in the group stage - but their consolation is that none of the previous four went on to win the tournament.
With United already having won Group F and Roma having qualified in second place the game had an eerie start, with the opening 20 minutes dreadfully apathetic.
David Pizarro tried to rid the match of its lethargy by shooting from 25 yards, but Tomasz Kuszczak dived away to his left to make a fairly routine save.
At the other end, United's youthful side fashioned their first opening when Wayne Rooney clipped in a cross from the right and Doni had to be alert to tip over John O'Shea's looping header.
Just after Mauro Esposito missed a golden chance with a close-range header for Roma, United took the lead.
The otherwise quiet Nani swung in a corner from the left and Pique sneaked in unchallenged six yards out to plant a header past Doni.
Mancini shot against the bar before equalising for Roma
The goal prompted a Roma rally as Mancini raised a shot from close-range on to the bar, Mauro Esposito headed the rebound over and then Mancini saw another effort parried away by Kuszczak.
The game was still being played at not much more than walking pace, but at least chances were being created.
United nearly doubled their lead after the interval when Chris Eagles helped another Nani corner goalwards, but a combination of Philippe Mexes and Doni managed to get the ball clear.
Ahmed Barusso came close to equalising, but his 25-yard belter just drifted the wrong side of the post with Kuszczak scrambling across his goalline.
Roma brought on Ludovic Giuly and Vucinic to chase the game and after Saha was denied by a fine Doni save, they pulled level.
Vucinic slotted the ball through to Mancini on the edge of the box and he neatly came inside and whipped his shot past the despairing dive of Kuszczak.
Vucinic was having a stunning impact on proceedings and the Montenegro striker rifled a shot against the foot of the post moments later.
Manchester United boss Sir Alex Ferguson on his young side's display:
"I was pleased with a lot of it, it was a very good experience.
"There wasn't a great deal at stake but both sides played with freedom and good expression and it was a good contest.
"We lacked experience at times but made up for it with ability on the ball and we can be happy against a strong team."
Roma: Doni, Cicinho, Ferrari, Mexes, Barusso (Giuly 62), Antunes, Pizarro, Esposito (Vucinic 62), Taddei (De Rossi 46), Mancini, Totti.
Subs Not Used: Bertagnoli, Panucci, Juan, Pit.
Goals: Mancini 71.
Man Utd: Kuszczak, Simpson, Pique, Evans, O'Shea (Brown 54), Eagles, Fletcher, Carrick, Nani, Saha, Rooney (Dong 71).
Subs Not Used: Heaton, Lee, Hewson, Brandy, Eckersley.
Goals: Pique 34.
Ref: Martin Hansson (Sweden).