Sabalenka praying for no more Wimbledon upsets after battling win
Several stars suffered shock first round exits from the All England Club, including second seed Coco Gauff, third seed Jessica Pegula and fifth seed Zheng Qinwen.
Top seed Sabalenka was pushed hard by Bouzkova in Wednesday's opening match on Centre Court as her Czech opponent matched fire with fire in a bruising encounter.
But she eventually had too much in her locker for her 48th-ranked opponent, firing an impressive 41 winners in a match lasting one hour and 35 minutes.
The Belarusian said after her win she was aware of the seeds who had crashed out but planned to focus on her own game.
"Honestly it's very sad to see so many top players losing in the first round but you better focus on yourself and stay away from the results," she said.
"I mean of course you're going to know the overall picture but it's better to take it one step at a time and do your best every time you're out here competing and I'm trying to stay away.
"I hope it's no upsets anymore in this tournament, if you know what I mean!"
The first set went with serve until Sabalenka doubled-faulted in the 11th game to hand Bouzkova the chance to serve for the set.
But the Belarusian broke back with a searing backhand down the line and came out on top in the tie-break to establish a foothold in the match.
Sabalenka broke again in the fifth game of the second set to move within sight of victory and closed out the match with little fuss.
She will face 2021 US Open winner Emma Raducanu or former Wimbledon champion Marketa Vondrousova in the third round on Friday.
Although Sabalenka is a three-time Grand Slam champion, she has suffered agonising three-set defeats in this year's Australian Open and French Open finals.
The 27-year-old has never been beyond the Wimbledon semi-finals and missed last year's tournament with a shoulder injury.