Djokovic finished off the veteran in three sets but only had an easy ride in the first, having to fight back from a break down in the second and settle for a tie-break victory in the third having been a break up.
Haas, blown off court in a 25-minute opening set, raised his game to break in the fifth game of the second set but Djokovic hit back to level at 4-4 with a cross-court backhand winner.
Normal service was soon resumed as Djokovic took the second set and moved 5-2 ahead in the third but Haas managed one last counter-attack to stretch the contest into a tie-break.
"I feel good about myself in this moment," Djokovic said. "I think I actually play better tennis on grass than I played two years ago when I won this tournament.
"I had a minor setback in the third set and I allowed him an opportunity to come back to the match. But I played a great tiebreak and I'm really glad to finish in three."
With the light fading and the prospect of the match being finished under the roof lights, there was an added sense of urgency as Djokovic bossed the tiebreak.
"If I had lost the third set and maybe they go on and close the roof and go under the lights deep in the night, you can't predict the result after that," he said.
He will now play Tomas Berdych for a spot in the semis after the Czech star's 7-6 6-7 6-4 6-4 win over Bernard Tomic.
A tight encounter was dominated by serve for the first two sets before seventh seed Berdych asserted his authority.
"Tough to play him so it makes me feel even better to be here as a winner," the Czech said after mastering the 20-year-old Australian, who had beaten seeds Sam Querrey and Richard Gasquet on the way to the last 16.
"I was kind of struggling with his fast routine on serve, I couldn't get a return on it at all. But after the first two sets I felt much more confident."
Berdych upset Djokovic in the semi-finals three years ago before losing to Rafa Nadal in straight sets in the final. That victory was just one of two he has enjoyed over the Serb, including the last time they met - in Rome on clay in May.
The Serb has triumphed in their 13 other meetings.
"It's a nice challenge," Berdych added. "I know how to beat him, let's try for the same."
David Ferrer wore down Croatia's Ivan Dodig with his high-energy scrambling to move into the Wimbledon quarter-finals with a 6-7 (3) 7-6 (6) 6-1 6-1 win on Monday.
The Spanish fourth seed arrived 10 minutes late on Court Two and was slow to impose himself on the match, losing the first set in a tiebreak before winning the second the same way.
Dodig, ranked 49th in the world, could not maintain his consistency as the match wore on and his serve, which had been such a weapon in the early stages, faltered to allow Ferrer to turn the screw.
After failing to win a point on the Dodig serve for four successive games in the second set, Ferrer broke three times in the third and twice in the fourth to wrap it up.
Ferrer, who has now reached seven successive Grand Slam quarter-finals, will next face eighth seed Juan Martin Del Potro.
Del Potro muscled his way into the Wimbledon quarter-finals with a powerful 6-4 7-6(2) 6-3 win over Italy's Andreas Seppi.
The Argentine's knee was heavily strapped following a nasty fall in his third-round match, but his slightly cumbersome movement was no barrier to a straight-sets demolition of the 28th-ranked Seppi.
He broke in the seventh game of the first set before wrapping it up in 52 minutes, stayed solid to come through the second in a tiebreak, before breaking in the second game of the third set to effectively end the Italian's resistance.
Poland has waited 33 years for a male quarter-finalist at a Grand Slam but two arrived within a few of minutes of each other at Wimbledon on Monday as Jerzy Janowicz and Lukasz Kubot set up an unlikely last-eight clash.
The big-serving Janowicz edged past Juergen Melzer 3-6 7-6 6-4 4-6 6-4, collapsing to the court in disbelief after finally subduing the Austrian veteran.
Then 130th-ranked Kubot launched into his party piece can-can dance routine to celebrate a 4-6 6-3 3-6 6-3 6-4 victory over fellow outsider Adrian Mannarino of France.
Janowicz, seeded 24, struggled to get to grips with the left-handed Melzer in the early stages on the tight confines of Court 12, but gradually turned up the heat.
Several exchanges with the umpire and even some back-chat with Melzer's courtside team fired up the towering Pole who produced some ear-splitting roars after winning crucial points.
When he broke Melzer's serve to lead 3-2 in the fourth set Janowicz seemed to have taken control but his concentration wavered and the 32-year-old Melzer hit back to drag an entertaining, and occasionally fractious, contest to a decider.
This time Janowicz got the break and did not falter to go one round better than last year when he reached the third round on his Grand Slam debut after qualifying.
The winner of his match against Kubot, who benefited from a walkover against Rafa Nadal's conqueror Steve Darcis in the second round, will be the first Polish man to reach a Grand Slam semi-final.
Wojtek Fibak was the last Polish man to reach a Grand Slam quarter-final, losing three times in the last eight in 1980.
Round four results
1-Novak Djokovic (Serbia) beat 13-Tommy Haas (Germany) 6-1 6-4 7-6(4)
2-Andy Murray (Britain) beat 20-Mikhail Youzhny (Russia) 6-4 7-6(5) 6-1
4-David Ferrer (Spain) beat Ivan Dodig (Croatia) 6-7(3) 7-6(6) 6-1 6-1
7-Tomas Berdych (Czech Republic) beat Bernard Tomic (Australia) 7-6(4) 6-7(5) 6-4 6-4
8-Juan Martin Del Potro (Argentina) beat 23-Andreas Seppi (Italy) 6-4 7-6(2) 6-3
24-Jerzy Janowicz (Poland) beat Jurgen Melzer (Austria) 3-6 7-6(1) 6-4 4-6 6-4
Fernando Verdasco (Spain) beat Kenny De Schepper (France) 6-4 6-4 6-4
Lukasz Kubot (Poland) beat Adrian Mannarino (France) 4-6 6-3 3-6 6-3 6-4