The fifth-seeded Russian, the only champion in the women's draw other than the Williams sisters, had 21 unforced errors and four double-faults in an inconsistent baseline performance in windy conditions on Court 2.
But, after falling behind 3-1 in the second set, Sharapova lifted her game to win five games in a row to finish off the 35th-ranked Czech player.
Zakopalova struggled with her footing, slipping at least four times along the baseline.
Sharapova pumped her fist and shouted "Come on!" after hitting a forehand service return winner to break for 5-3 in the second set, then finished the match in the next game with another forehand winner down the line.
Sharapova, who won Wimbledon in 2004 at age 17, hasn't reached the semifinals since 2006. She will next face 20th-seeded Peng Shuai of China, who beat Melinda Czink of Hungary 6-2, 7-6 (5).
In other play Saturday, defending champion Rafael Nadal resumed his third-round match on Court 1 against Gilles Muller of Luxembourg. The top-seeded Spaniard was leading 7-6 (6) when the match was suspended by rain Friday.
Due to follow on Court 1 was four-time women's champion Serena Williams against Maria Kirilenko and fifth-seeded Robin Soderling against Australian teenager Bernard Tomic.
Top-seeded Caroline Wozniacki, still looking for a first Grand Slam title, was opening first on Centre Court against Jarmila Gajdosova. Six-time champion Roger Federer was up next against David Nalbandian, followed by No. 2 Novak Djokovic vs. Marcos Baghdatis.
With the help of an audacious between-the-legs trick shot, Andy Murray will head into the second week of Wimbledon again carrying the hopes of a nation for a first homegrown men's champion in 75 years.
The fourth-seeded Murray advanced to the fourth round by defeating Ivan Ljubicic 6-4, 4-6, 6-1, 7-6 (4) in a match that ended at nearly 10 p.m. Friday under the roof on Centre Court.
Rather than Murray's big serve or two-handed backhand, the talk was all about the shot he pulled off in the seventh game of the fourth set.
After Ljubicic hit a short ball, Murray strolled forward toward the service line, hopped in the air, took his racket behind his back and casually flicked a shot through his legs. It floated over the net and landed in for a cross-court winner.
It was similar to a shot Murray hit during his victory over Jo-Wilfried Tsonga in the final of the Queen's Club grass-court tournament on June 13.
"It's just one of those things that you're just in the right position," Murray said. "I tried it at Queen's and I tried it a couple of times in practice since. I haven't missed one yet. You look like a plonker (fool) when you do, so I'm glad I made it.
"It's one of those shots that you don't get a chance to try them very often and, luckily, I've pulled it off a couple times the last few weeks."