But despite a scoreline which leaves United clear at the top of Group F, Sir Alex Ferguson's side were again far from convincing in Europe.
Before the match Ferguson had promised an improved display from the one that saw United dumped out of the Champions League at the group stage by Benfica last season.
But in truth for large sections of the game the home side were on top and looked the most likely to score until Saha's scintillating 60th minute strike.
Cristiano Ronaldo forced a good save from Quim after 14 minutes when he came deep to collect a pass before turning and dispatching a low drive.
But with Saha often left isolated up front and Michael Carrick and John O'Shea struggling to control the midfield area, it was Benfica who dominated the opening period.
United had Edwin Van der Sar to thank for keeping the scores level on the half-hour mark when he threw himself across goal to tip a vicious Nuno Gomes drive around the post, after Nemanja Vidic had carelessly lost the ball on the halfway line.
After the break United started to find their rhythm in attack and Carrick tested the keeper with a low drive after combining well with Paul Scholes.
United grew in confidence and the breakthrough arrived on the hour-mark courtesy of some intelligent play from Ronaldo.
The Portugal international broke over the halfway line and fed Saha who ran towards goal before cutting back on to his favoured left foot and lofting a drive over the keeper from the corner of the penalty area.
Saha should have doubled his and United's tally in the 78th minute when he met Carrick's near-post cross with a first-time effort which flashed the wrong side of the upright.
Five minutes from time Alan Smith made his long-awaited return to first-team action following an horrendous leg injury as a replacement for Saha, while the worryingly ineffective Rooney was replaced by Darren Fletcher.
And Fletcher should have scored in the dying minutes, but Quim made a superb series of saves to first block Gabriel Heinze's free-kick and then follow-ups from both the Scotland international and Carrick.