Swiatek, who won the French Open title for the third time last month to make it four Grand Slam crowns, has yet to get past the fourth round of the London major.
Swiatek, 22, looked good in her movement on the surface and showed no signs of any effects of the illness that had ruled her out of her Bad Homburg semifinal on Friday.
“I felt really confident. I felt like I did a very good job,” said Swiatek, a former junior champion at Wimbledon. “I feel really good after Roland Garros. After Roland Garros I took some time to appreciate what happened.
“Last year it was my second Grand Slam [at the French Open], and it felt overwhelming. This time I could focus on celebrating and actually at getting back to work with more peace in my head.”
Zhu, ranked 34th in the world, earned a break point in the first game but Swiatek won 11 points in a row to sprint into a 3-0 lead.
Another break put Swiatek, a renowned slider on clay and hard courts who has often struggled with her movement on grass, firmly in the driving seat.
Zhu saved two set points at 5-0, but Swiatek sealed the first set a game later with a powerful crosscourt forehand winner.
Play was interrupted due to rain in the second set but resumed after the roof on Court One was shut. Once back on the court, Swiatek needed only seven minutes to win the two games she needed and sealed victory with a backhand winner.
Swiatek wasn’t the only high seed to triumph. American Jessica Pegula, the fourth-ranked woman in the world, reached the second round with a hard-fought 6-2, 6-7 (8), 6-3 win over compatriot Lauren Davis on Monday.
Davis struggled to find her range from the start and was broken in the first game. That set the tone for the next few games as she racked up the unforced errors and Pegula raced into a 4-0 lead in less than 15 minutes.
Davis finally found her forehand power to get on the scoreboard, but Pegula’s pinpoint backhand meant she never got close to breaking back. The Australian Open quarterfinalist wrapped up the first set comfortably.
It was a different story in the second set, Davis making sure she held serve in the opening game with a couple of drop shots, forcing Pegula to go long, and held again to lead 2-1.
Both players struggled with a gusty wind at times, but Davis began spraying the ball across the court with power and precision. A close second set lasting over an hour went to a tiebreak, with Davis winning to level the match.
Neither player looked entirely comfortable on the Court Two lawn, each making more than 30 unforced errors in total. But Pegula got the crucial break in the decider to lead 5-3 when Davis hit a backhand into the net.
Pegula closed out the match with a high backhand volley to advance to the second round where she will face Spain’s Cristina Bucsa.
“Definitely a tough match. I think Lauren is a good grass-court player. Obviously, she’s had great results here before, beating [Angelique] Kerber a few years ago,” Pegula said.
“I hit kind of flat, so it stays low for her, especially on the grass,” she added.
“It was very windy, so it was hard to really feel like you could get any momentum going because then you’d have the wind gusting. It would kind of keep you off balance and unstable,” she added.
Information from Reuters was used in this report.
Iga Swiatek, American Jessica Pegula advance at Wimbledon