At No. 3, Halep is the highest seed left in the tournament and needed only 51 minutes to complete the second-round match.
Before Wimbledon she won her first WTA titles in Germany and the Netherlands.
"I think I'm in my best form ever," Halep said.
"Everything seems to be working perfectly — my body and my game."
She will face Hungary's top female player, Timea Babos, who beat seventh-seeded Maria-Teresa Torro-Flor of Spain 1-6, 6-4, 7-6 (4).
Fourth-seeded Annika Beck of Germany defeated Lucie Hradecka of the Czech Republic 6-3, 6-3.
Beck's opponent in the quarter-finals will be Yvonne Meusburger of Austria, who rallied to upset fifth-seeded Johanna Larsson of Sweden 3-6, 6-4, 6-4.
Results from the third day of the WTA Budapest Grand Prix (x denotes seeding):
Second round:
Annika Beck (GER x4) bt Lucie Hradeck (CZE) 6-3, 6-3
Yvonne Meusburger (AUT) bt Johanna Larsson (SWE x5) 3-6, 6-4, 6-4
Simona Halep (ROM x3) bt Agnes Bukta (HUN) 6-1, 6-1
Tmea Babos (HUN) bt Mara Teresa Torr (ESP x7) 1-6, 6-4, 7-6 (7/4)