World number one Nadal, fresh from his record-equalling sixth French Open title, looked in total command against Stepanek as he served for the match in the second set.
However, a rare collapse kept the Spaniard on court for longer than he wanted before he walked off with a 6-3, 5-7, 6-1 victory.
"For sure, I'm a bit tired," Nadal said on court before hurrying off to play doubles with partner Marc Lopez.
"5-2, 5-3, 40-15 he played well. I had a few mistakes and you know that's the turning point.
"The beginning of the third was tough but after that I think I played my best. Much better than yesterday."
Second seed Murray, who will spend the next few weeks shouldering Britain's hopes of a first men's grand slam champion since 1936, beat flashy Serb Janko Tipsarevic 6-4, 7-6 despite losing his service at the start of each set.
Roddick, the third seed who is looking for a record fifth title at the traditional Wimbledon warm-up event, was equally impressive as he dispatched towering South African Kevin Anderson 6-4, 6-4 to set up a quarter-final against Spain's Fernando Verdasco, a 7-5, 6-1 winner against David Nalbandian.
Another Argentine to fall was Juan Martin del Potro, who was bundled out in two tiebreaks by Frenchman Adrian Mannarino.
Croatia's Marin Cilic made it a bad day for south Americans as he ousted Brazil's Thomaz Bellucci 7-6, 0-6, 6-3 to seal a last-eight clash against Murray.
Nadal is usually ruthless when an opponent is on the ropes, but serving at 5-3 in the second set he wasted two match points and then threw in a double fault to give Stepanek a lifeline.
Then, at 5-5, he played another messy game and suddenly the mercurial Czech veteran was serving for the second set, which he did in some style, levelling the match with a lunging volley.
While the crowd, some of them perched on the balconies of the rambling Victorian clubhouse, loved it, Nadal was clearly not amused and stormed through the deciding set in quick time to set up a last eight meeting with fifth seed Jo-Wilfried Tsonga.
Murray's ankle improving
Murray, beaten by Nadal in last year's Wimbledon semi-final as the Spaniard marched towards a second title at the All England Club, made sloppy starts to each set against the bespectacled Tipsarevic.
The Scot appears to like setting himself puzzles to solve though and the way he recovered both times with some dazzling shot-making and thumping serves left him feeling upbeat.
Even better news was his suspect right ankle, injured at the French Open, showed signs of improvement.
"It's the best it's felt," world number four Murray, who won the Queen's title in 2009, told reporters.
"If I had gotten off to better starts I could have won more easily but I was always trying to get myself back into it. I did a good job of that."
American Roddick, who has won four titles at Queen's but never gone on to reach the Holy Grail at Wimbledon, required just one break of serve in each set to get the better of the 2.03-metre Anderson, one of the most improved players on the Tour.
After an impressive victory against dangerous Feliciano Lopez in the previous round, the third seed said he was happy with his form at his favourite time of the year.
"Everything felt fine," said Roddick, three-times a Wimbledon runner-up to Roger Federer.
"He had some chances to break. He didn't get them. I had a couple chances and I converted. That was pretty much the story of the match," added Roddick, who fired down two 225kph bullets towards the end of the match, proof that his famed serving shoulder is in fine fettle.
Two French players were forced to withdraw injured.
Gilles Simon retired with a back strain at 3-0 down in the third set against compatriot Mannarino in a second-round match held up overnight and Michael Llodra quit with a thigh injury in the first set against Tsonga.
-ReutersTags: sport, tennis, united-kingdom, england