The Czech, a quarter-finalist at the Australian Open last year, was one of the form players on the WTA Tour in the latter end of last season after she returned from an elbow injury.
The former world number two was clearly not at her very best against the American lucky loser and needed a tiebreak to finally finish off her opponent after being broken when serving for the match.
Krejcikova, now 22nd in the world, will have a tougher test in her next match when she faces Russian world number eight Daria Kasatkina, who received a bye into the second round.
World number nine Veronika Kudermetova is another player who came into the new season with high expectations and she showed why when she rallied from 3-0 down in the second set tiebreak to beat Victoria Azarenka 2-6 7-6(4) 6-4.
Azarenka needed treatment on a sore neck in the third set but Kudermetova had to battle it out for nearly three hours in sweltering heat to beat the twice Australian Open champion.
"I am really happy with this win," said the Russian. "Vika is a Grand Slam champion and for me, it is very important to play that kind of player and beat them.
"With every win, I get a little bit more confidence."
The 2017 French Open champion Jelena Ostapenko had a less successful day, going down 6-3 6-4 to Russian qualifier Anna Kalinskaya.
Former Australian Open champion Sofia Kenin was in action at the other warm-up for the year's first Grand Slam and looked in good touch as she beat China's Zhu Lin 6-2 6-2 in the opening round of the Hobart International.
"I felt really good, conditions were a little bit tough but I felt like I played a solid match so I'm super happy," said Kenin, who will play second seed Elise Mertens or qualifier Maryna Zanevska in the next round.
"I played here a few years ago so I'm kind of used to this weather so I'm just trying to use this to my advantage."
She won her first WTA title in Hobart in 2019 and returned to Australia the following year to claim a Grand Slam title at Melbourne Park.
Little has gone right for the one-time prodigy since with illness, injury and off-court issues precipitating a tumble down the world rankings.
"I feel like I'm getting there," Kenin, now ranked 143rd, added. "I'm happy with the way I'm starting, knock on wood; I'm healthy, injury-free, so I'm just going to continue doing my best."
Another former Hobart champion, French third seed Alize Cornet, earlier crashed out in a 6-4 6-2 loss to Italian Elisabetta Cocciaretto.