Sharapova, the 2006 winner at Flushing Meadows, appeared out of sorts on blustery centre court that earlier claimed fourth seed Agnieszka Radwanska, committing 22 unforced errors on way to dropping the first set to her 95th ranked Romanian opponent.
But in the second set the French Open champion slowly took charge, breaking Dulgheru to go up 4-2 before shifting into top gear and sweeping through five straight games to clinch the set and race to a 4-0 lead in the third.
Sharapova will next face the winner between American Madison Brengle and German Sabine Lisicki.
Peng Shuai of China upset fourth-seeded Radwanska of Poland 6-3 6-4. The 28-year-old Peng, the doubles world number one, used her piercing, two-fisted groundstrokes to put Radwanska on the defensive and claimed the biggest scalp of the championship on her third match point with a backhand crosscourt winner.
Peng, the French Open doubles champion who is looking for her first career WTA Tour title, registered 28 winners in the 96-minute match.
The unseeded Chinese, ranked 39th in singles, will play 28th seed Roberta Vinci after the Italian's 2-6 6-4 6-1 win over Irina-Camelia Begu of Romania .
Peng Shuai of China hits a return to Agnieszka Radwanska of Poland during their match at the 2014 US Open (Reu …
Johanna Larsson of Sweden, ranked 96th, sent another seed to the exits with a 5-7 6-4 6-2 upset of 21st-seeded American Sloane Stephens, a 2013 Australian Open semi-finalist.
Halep, who battled back to beat US college champion Danielle Collins in the opening round after losing a first-set tiebreaker, wasted little time as temperatures soared on a hazy day in Flushing Meadows.
"I started a little bit too slow, but then I started to be more aggressive and hit the ball," said world number two Halep. "I feel great now that I could win so fast today because it's so hot outside."
The 34-year-old, seven-times Grand Slam winner reached the round for the first time in four years at Flushing Meadows through a 6-1 6-4 victory on the Arthur Ashe Stadium court which she helped christen with the first Open final there in 1997.
"I was watching Serena last night and she played so well so I tried to do the same thing," twice US champion Venus said about her 32-year-old, number one-ranked sister, who blazed by fellow American Taylor Townsend in straight sets on Tuesday.
"I'm really happy to have pulled it out in the end," added Venus, who will play Italian 13th seed Sara Errani who beat Australian Anastasia Rodionova 6-4 7-6 (2).
Williams charged through the first set, but the next set stayed on serve until the ninth game when the 78th-ranked Swiss hit a wayward backhand wide to put the American 5-4 ahead.
With Williams serving for the match, Bacsinszky reached break point at 30-40 threatening to put the match back on serve.
But the 19th-seeded Williams then powered in a 96mph second serve, her fastest second serve of the match, for a winner.
US Open results
19-Venus Williams (U.S.) beat Timea Bacsinszky (Switzerland) 6-1 6-4
6-Angelique Kerber (Germany) beat Alla Kudryavtseva (Russia) 6-2 6-4
Belinda Bencic (Switzerland) beat 31-Kurumi Nara (Japan) 6-4 4-6 6-1
Johanna Larsson (Sweden) beat 21-Sloane Stephens (U.S.) 5-7 6-4 6-2
9-Jelena Jankovic (Serbia) beat Tsvetana Pironkova (Bulgaria) 7-5 6-4
14-Lucie Safarova (Czech Republic) beat Zheng Saisai (China) 6-3 4-6 6-2
22-Alize Cornet (France) beat Daniela Hantuchova (Slovakia) 6-3 6-3
28-Roberta Vinci (Italy) beat Irina Begu (Romania) 2-6 6-4 6-1
Peng Shuai (China) beat 4-Agnieszka Radwanska (Poland) 6-3 6-4
18-Andrea Petkovic (Germany) beat Monica Puig (Puerto Rico) 3-6 6-3 7-6(5)
10-Caroline Wozniacki (Denmark) beat Aliaksandra Sasnovich (Belarus) 6-3 6-4
Mirjana Lucic-Baroni (Croatia) beat Shahar Peer (Israel) 6-7(6) 6-3 6-2
2-Simona Halep (Romania) beat Jana Cepelova (Slovakia) 6-2 6-1
- Sports & Recreation
- Agnieszka Radwanska
- Venus Williams
- Simona Halep
- Australian Open
- Roberta Vinci
- Timea Bacsinszky