The Russian fifth seed and five-time grand slam champion edged to a 4-6 6-3 6-2 victory over Romanian Dulgheru at Flushing Meadows.
Sharapova struggled early but eventually got the job done, albeit unconvincingly, in two hours 38 minutes.
The 2006 US Open winner hit 34 winners to go with 46 unforced errors, with either German 26th seed Sabine Lisicki or American Madison Brengle awaiting her in the third round.
An error-riddled opening set went Dulgheru's way after the duo combined for 34 unforced errors in 67 points.
Sharapova never reached any great heights, although she did lift briefly to run away early in the deciding third set.
Dulgheru battled a wrist injury during the final set and never looked like threatening Sharapova despite the latter being below her best.