The No.2-seeded Halep lost a pair of marathon games at the start of the match to fall behind 2-0, but she soon found her bearings, winning 12 of the next 14 games to beat the Swedish wildcard, 64 60.
"I didn't know my opponent before the match, but she played really well," Halep said. "She's a tough, strong player. If she keeps playing like that and improving she will do big things in the future."
Halep has been on a big roll over the last several weeks, winning her first three WTA titles at Nürnberg, 's-Hertogenbosch and Budapest, reaching the second round of Wimbledon in between (falling to Li Na in three sets), and now winning her Bastad opener. She has a 17-1 record since the French Open.
"It was a bit difficult to play today because I'm a little bit tired, but I'm feeling good physically and with my game, so I'm just trying to enjoy every match," Halep said. "I'm not feeling any pressure though. I'm just trying my best out there and trying to enjoy the tournament, playing relaxed with no stress."
When this week is done, will Halep finally take a break? "I'll be taking a week off, maybe I'll just go back to my hometown with the beach and everything," she said. "I haven't treated myself yet for all of these results, I haven't had time! But I will. I'm not sure how. Probably some shopping or something."
But before that, there's more work to do in Bastad - she has a difficult second round clash against former Top 10 player Flavia Pennetta, against whom she lost their only previous meeting in 2010.
"I have to be more aggressive in the next match," Halep said. "She's very good. She was a top player. I also have to relax because if I'm nervous she'll beat me for sure. I have to be calm and enjoy it."
Halep's match was the last first round match to be played at the International-level tournament.
The first four second round matches were also on the Wednesday schedule, with the three seeds in action all advancing: No.3 seed Klara Zakopalova took just 61 minutes to beat Arantxa Parra Santonja, 63 61, her first win in their four career meetings; No.5 seed Lourdes Domínguez Lino rallied from 4-2 down in the second set and 3-1 down in the third set to edge Teliana Pereira in a two-hour, 29-minute thriller, 36 64 63; and No.8 seed Johanna Larsson outclassed Nina Bratchikova in 69 minutes, 62 63.