The English champions wasted little time getting off the mark, Valencia striking in the eighth minute, but they failed to kick on with a lacklustre performance.
Nerves were tested on a mild Old Trafford evening as United's big guns misfired against the competition debutants from Romania before Wayne Rooney made sure of victory with a late deflected strike.
United moved to eight points with two group games to go, putting last season's runners-up firmly on course for the knockout stages once again.
The Old Trafford crowd, keen to erase memories of the 6-1 hammering by Manchester City in the last match on this pitch, must have been thinking of a rout after the early goal and seeing their team's attacking lineup.
United went in front when Dimitar Berbatov's pass found Phil Jones on the right and the defender's cross was tapped in by Valencia after it was missed by a charging Michael Owen.
That was the last action for Owen who limped off with a thigh injury three minutes later as the hosts were forced into an 11th-minute substution, bringing on Javier Hernandez.
United had the time, the space and the possession but could not muster a second goal in the first period despite a couple of chances for right back Jones, who spent most of his time attacking, Fabio and Anderson.
The Romanian champions laid their cards on the table when they named six defenders in their lineup and waited until just before the break to test United keeper David de Gea.
The Spaniard easily caught Ionut Neagu's speculative shot from distance before doing to well to bat away a deflected effort from the midfielder soon afterwards.
The restless home crowd got ever quieter as second-half chances went begging for Nani and Rooney, who was playing in central midfield.
Anderson had a glorious chance from the edge of the box but Galati centre back Sergiu Costin dashed back to hoof the ball off the line and keep his side in the game.
Berbatov was left berating himself after shooting into the side netting with only keeper Branko Grahovac to beat with a quarter of an hour left as the tension mounted before Rooney secured the points with a deflected shot.
Results
Group A: Villarreal 0, Manchester City 3; Bayern Munich 3, Napoli 2.
Group B: Inter Milan 2, Lille 1; Trabzonspor 0, CSKA Moscow 0.
Group C: Benfica 1, Basel 1; Manchester United 2, Otelul Galati 0.
Group D: Olympique Lyon 0, Real Madrid 2; Ajax Amsterdam 4, Dinamo Zagreb 0.
