The second seed, 32, converted his third match point to win 6-3 6-3 6-4.

The Spaniard is still on track to meet top seed Roger Federer - on the 10th anniversary of their epic 2008 final - in Sunday's men's singles showpiece.

Nadal will play either Argentine fifth seed Juan Martin del Potro or France's Gilles Simon in the last eight.

The 17-time Grand Slam champion is playing his first tournament since winning an 11th French Open title last month after pulling out of Queen's - a move that appears to be paying dividends.

Nadal looks refreshed and in peak condition both mentally and physically having not dropped a set on his way to the quarter-finals.

"It is an important moment for me. I'm happy to be where I am and playing well," he told BBC Sport.

"They have been four positive matches, I haven't played on grass for a year and I'm hoping to keep enjoying it."

No danger of a shock loss for Nadal

Nadal has won Wimbledon twice - in 2008 and 2010 - but has also suffered some shock defeats on what is his least natural surface.

Since finishing runner-up to Novak Djokovic in 2011, Nadal has been knocked out by four players ranked outside the world's top 100 - Lukas Rosel, Steve Darcis, Nick Kyrgios and Dustin Brown - as well as a surprise defeat by Luxembourg's Gilles Muller last year.

But there was never any danger of that happening against world number 93 Vesely.

Nadal moved into a 3-1 lead in the opening set when Vesely coughed up a double fault on the first break point of the match, an error that proved significant given the underdog was unable to make a dent on Nadal's service game.

Indeed the 24-year-old, aiming for his first Grand Slam quarter-final, won just two points on Nadal's serve in an opening set that lasted 31 minutes.

A single break was also enough for Nadal to move into a two-set lead shortly after the hour mark and, with the Majorcan having only ever lost one Grand Slam match from that position, it looked unlikely Vesely would cause a shock.

Stars shine on Centre Court

With Federer and Serena Williams both cruising through in straight sets before Nadal began his match, the Centre Court crowd was hoping to see more of a contest in the day's third and final singles.

But with Nadal looking untroubled as he claimed the first two sets, the lull around Wimbledon's show court showed no signs of lifting.

Eventually there was a spark when Vesely threatened to push the match into a fourth set by earning his first break point of the match out of nowhere.

It was even more surprising when Nadal walloped a relatively simple forehand into the net to give Vesely a 3-2 lead.

That error only served to sharpen Nadal's focus, however, as he broke straight back in the next game and took Vesely's serve again - albeit after some admirable resistance - to win in one hour and 53 minutes.

"He started to play better from the baseline, I made a couple of mistakes," said Nadal.

"But then I came back - that was a key moment in that third set."