The Romanian has enjoyed a strong record at grand slams in 2014, reaching the quarter-final, semi-final and final of the Australian Open, Wimbledon and the French Open respectively.
Seeded second for the tournament in New York, Halep is fancied to go deep at Flushing Meadows over the next fortnight.
And there were positive signs on Wednesday as Halep saw off world number 65 Cepelova in just under an hour.
Halep made a strong start at Louis Armstrong Stadium, breaking in the second game courtesy of an unforced backhand error from her opponent.
Cepelova hit back immediately to move the set back on serve, but breaks in games five and seven from Halep saw her pull further clear, sealing a one-set lead with an ace.
Halep continued her dominance in the second set and took the initiative as another unforced error from Cepelova in game three handed the world number two a break.
She built upon that with another in game five, before sealing her passage through to the third round with a third successive break as Cepelova sent a backhand long.