كتب : Hatem Maher
The Argentinean dived to head home Owen Hargreaves cross in the 70th minute and ensure United's superiority over the Italian side after a 2-0 victory in the first leg.
The Red Devils, who last won Europe's premier competition in 1999, will face Barcelona in the semi-final after the Catalans overcame Germany's Schalke.
United coach Alex Ferguson surprisingly left key trio Wayne Rooney, Cristiano Ronaldo and Paul Scholes on the bench.
However, Roma could not take advantage of facing a relatively weakened United side.
Korean winger Ji-Sung Park could have put the hosts in front after six minutes when he latched onto Ryan Giggs' pass but his shot from inside the area went across goal.
Four minutes later, Hargreaves went clear on goal after picking up another deft pass from Giggs.
Roma keeper Alexander Doni rushed out to block the English midfielder effort and keep his side's hopes alive.
The lively Hargreaves had another opportunity midway through the first-half but Juan and Marco Cassetti intercepted to clear the danger.
Roma were awarded a deserved penalty in the 29th minute when Wes Brown sloppily brought down Brazilian winger Mancini inside the area.
Daniele De Rossi stepped-up but blasted his shot wide as Roma failed to narrow the deficit.
Tevez broke the deadlock in the 70th minute when he escaped Philippe Mexes to head Hargreaves' pinpoint cross past Doni.
United right-back Gary Neville made his first appearance for over a year after a series of injuries kept him on the sidelines.
He replaced Brazilian midfielder Anderson nine minutes from time.