After the high-profile departures of Rafael Nadal, Roger Federer and Maria Sharapova in the first week, Kvitova sneaked through on a blustery Court Three before the main fourth-round action had started on the big show courts.
It was not all plain sailing for the 2011 champion, who has yet to rediscover the consistency that took her to world number two 20 months ago.
"I was pretty nervous today...I didn't play my best, especially in the first set. But it's important to win the last point which was what I did," Kvitova told a news conference.
Suarez Navarro, 24, the last Spanish woman in the draw, harried her from the baseline, moving fast, returning early and chasing down the Czech's booming groundstrokes.
She was watched in the stands by Fed Cup captain Conchita Martinez, the only Spanish woman to win the Wimbledon title when she beat Martina Navratilova in the 1994 final.
Eighth seed Kvitova, 23, broke the Spaniard's serve and should have finished off the first set in the 12th game but nervy shots allowed Suarez Navarro to break back, using her rare and elegant single-handed backhand to stinging effect.
With big names like the injured Victoria Azarenka and former world number one Caroline Wozniacki gone, Kvitova was clearly feeling the weight of expectation.
"Everybody is talking about that I'm the highest seeded player in my half, I'm supposed to be already in the final. It's not really easy to hear that," she said.
But the statuesque Czech's power eventually proved too much for her more diminutive opponent and she pressured Suarez Navarro into slapping a forehand into the net to take the set 7-5 in the tiebreak.
Emerging victorious from a tight tiebreak appeared to energise Kvitova and she bowled through the second set in 34 minutes, using her big left-handed serve, long reach and strength to quell her Spanish opponent.
Kvitova will play 20th seed Kirsten Flipkens in the quarter-finals on Tuesday.
"I lost against her last time in Miami. So I hope that I can play better tennis than in the last match," she said.
"We've never played on the grass, which is quite difficult."
Men's singles:
Fourth round:
Novak Djokovic (SRB x1) bt Tommy Haas (GER x13) 6-1, 6-4, 7-6 (7/4)
Tomas Berdych (CZE x7) bt Bernard Tomic (AUS) 7-6 (7/4), 6-7 (5/7), 6-4, 6-4
David Ferrer (ESP x4) bt Ivan Dodig (CRO) 6-7 (3/7), 7-6 (8/6), 6-1, 6-1
Juan Martn Del Potro (ARG x8) bt Andreas Seppi (ITA x23) 6-4, 7-6 (7/2), 6-3
Lukasz Kubot (POL) bt Adrian Mannarino (FRA) 4-6, 6-3, 3-6, 6-3, 6-4
Jerzy Janowicz (POL x24) bt Jurgen Melzer (AUT) 3-6, 7-6 (7/1), 6-4, 4-6, 6-4
Fernando Verdasco (ESP) bt Kenny De Schepper (FRA) 6-4, 6-4, 6-4
Andy Murray (GBR x2) bt Mikhail Youzhny (RUS x20) 6-4, 7-6 (7/5), 6-1
Women's singles:
Fourth round:
Sabine Lisicki (GER x23) bt Serena Williams (USA x1) 6-2, 1-6, 6-4
Kaia Kanepi (EST) bt Laura Robson (GBR) 7-6 (8/6), 7-5
Agnieszka Radwanska (POL x4) bt Tsvetana Pironkova (BUL) 4-6, 6-3, 6-3
Li Na (CHN x6) bt Roberta Vinci (ITA x11) 6-2, 6-0
Sloane Stephens (USA x17) bt Monica Puig (PUR) 4-6, 7-5, 6-1
Marion Bartoli (FRA x15) bt Karin Knapp (ITA) 6-2, 6-3
Petra Kvitova (CZE x8) bt Carla Surez (ESP x19) 7-6 (7/5), 6-3
Kirsten Flipkens (BEL x20) bt Flavia Pennetta (ITA) 7-6 (7/2), 6-3