Halep's recent events have included her first Premier-level semifinal in Rome, her first WTA title on the red clay of Nürnberg and another WTA title the very next week on grass in 's-Hertogenbosch. Though she fell to then-World No.6 Li Na in the second round of Wimbledon, she extended the eventual quarterfinalist to three sets.
In her Budapest opener against Sesil Karatantcheva, the third-seeded Halep won nine straight games from 3-3 in the first set for a 63 60 triumph in 51 minutes. Dating back to Rome qualifying, she has now won 18 of her last 21 matches.
"It was a good match for me," Halep said. "The first round is always difficult. At 3-0 in the first, I was a little nervous and wanted to finish fast because I was waiting a lot today, but I came back and won.
"It's nice to play on clay because I love this surface. I played well on grass, but I feel better on clay."
Next up for Halep is Hungarian 19-year-old Agnes Bukta, who in her very first WTA match was a 61 46 76(4) winner over Sandra Zahlavova in 10 minutes short of three hours.
Also moving on was No.5 seed Johanna Larsson, who overcame a set point down 5-4 in the second set of her 62 75 defeat of Lara Arruabarrena and had to be treated for a lower back injury right before serving for the match at 6-5.
"I'm feeling okay," Larsson said. "I hurt my back a little bit. I just wanted to check it and have a talk with the physio and see what she said, so hopefully it won't be a problem for me the rest of the tournament."
Larsson's victory snapped a three-match losing streak in which the Swede did not win more than three games in any set.
"I cannot be more happy about leaving the grass behind. I'm more comfortable and happier about playing on the clay. It's a more positive atmosphere for me."
Among those in first round action Tuesday are No.1 seed Lucie Safarova and No.2 seed Alizé Cornet, who won her first WTA title here in 2008 and is the only former Budapest champion in this year's field.