The 21-year-old French winger failed to find the target in 13 appearances last season after joining from Bordeaux but broke his duck with a neat second-half finish at Lincoln Financial Field.
Obertan savoured the moment in front of a crowd of 44,213 as United posted a second successive victory on their five-match tour following on from their 3-1 triumph against Celtic on Friday.
A youthful United line-up saw Federico Macheda paired with fellow teenager Danny Welbeck in attack, and Ferguson's troops were quickly into their stride.
United almost opened the scoring in the third minute when Obertan was released by Macheda. Obertan took a touch but saw his effort blocked by Jordan Harvey.
The busy Obertan was then left unmarked at the back post in the eighth minute as Welbeck delivered the cross with Fabio also playing a part in a swift counter-attack. The Frenchman failed to test goalkeeper Brad Knighton, though, as his volley went wide.
The MLS side responded and might have gone ahead in the 12th minute had Alejandro Moreno not scuffed his shot to present Tomasz Kuszczak with a comfortable save.
It was brief respite for the hosts and Paul Scholes, paired with Tom Cleverley in the heart of midfield, soon sent Obertan clear only for the move to break down.
Welbeck showed good skill to create an opening in the 32nd minute but his shot from 25 yards went narrowly wide, while the Union were grateful to Knighton for keeping them on level terms five minutes later as he made a superb block from Welbeck's shot.
Scholes' enthusiasm got the better of him in the 40th minute and he was booked after taking the legs of Eduardo Coudet.
A minute later Sebastien Le Toux saw his shot beat Kuszczak only for the ball to sail the wrong side the post.
Welbeck's pace and movement were causing the Union defence problems and he thumped a shot wide just a minute into the second period.
The game opened up after the break and Macheda fired a shot over the bar in the 58th minute as the visitors began to turn the screw.
United were indebted to Kuszczak for keeping the score level in the 69th minute when the keeper reacted superbly to parry clear Kyle Nakazawa's goalbound free-kick.
United made the breakthrough 14 minutes from time as the impressive Obertan was rewarded for his toil, clipping home a effort from close range after being played in by Welbeck.
Substitute Dimitar Berbatov almost doubled United's lead four minutes later but was unfortunate to see his instinctive effort hit the underside of the bar and bounce clear.
Substitute Andrew Jacobsen should have pulled the Union level at the death but skied his effort over the bar as United held on.