The world No. 1 from Scotland has dropped just 14 games in his first two rounds at the All England Club in London. He has reached at least the third round in all 12 of his appearances at the Grand Slam grass-court event.
The defending champion hit 31 winners to just five unforced errors, breaking the German five times to advance in one hour, 36 minutes.
"He started the match very well but I found my way into it and was able to get to some of his drop volleys and make some passing shots," Murray said afterward. "Until right at the end I was serving well and getting lots of free points. He couldn't really attack my second serve and moved well too."
The 30-year-old Murray came into the tournament slowed by a hip injury.
"The hip feels OK," Murray said. "I moved well first couple of matches and I've been getting good practices in. I feel good and so far feel very good.
"I've played two guys with tough game styles. It's been a good start and hopefully I can keep things going."
Awaiting Murray in the next round is No. 28 seed Fabio Fognini, who moved past Jiri Vesely of the Czech Republic 7-6 (3), 6-4, 6-2.
Fognini fired 11 aces and didn't drop serve to prevail in one hour, 47 minutes.
Murray and Fognini are even in head-to-head matches at 3-3, but have never played at a Grand Slam or on grass. Fognini won their most recent encounter in May at the event in Rome.
Nadal, who is a two-time Wimbledon champion, reached the third round of the tournament for just the second time since 2011.
While his recent track record at the All England Club may not be sterling, Nadal's recent play has been quite impressive. He did not lose any of the 20 sets he played en route to winning his record 10th French Open championship last month, and he has continued that stretch with straight set victories at Wimbledon.
Nadal's victory over Young propelled the veteran into a match against Karen Khachanov, who beat Brazilian Thiago Monteiro 3-6, 7-6 (5), 7-6 (3), 7-5. The 21-year-old Russian, who is making his Wimbledon debut, has pieced together solid outings on grass over the last month -- including a semifinal appearance at the Gerry Weber Open in Halle.
The German broke in the first game of the match and had an opportunity to serve for the first set, but Cilic hammered three aces to emerge victorious in the tiebreak. Cilic kept up the intensity, recording four winners to break in the ninth game of the second set and finished off the contest with an ace.
Ninth-seeded Kei Nishikori of Japan notched a 6-4, 6-7 (7), 6-1, 7-6 (6) win over Sergiy Stakhovsky of the Ukraine.
"I knew it was going to be a tough match because Sergiy's best surface is grass," the 27-year-old Nishikori said. "The last set was very tough. It was hard to get a break."
Nishikori advances to face No. 18 Spaniard Roberto Bautista Agut, who also needed four sets to advance with a 6-2, 6-1, 3-6, 6-3 triumph over German Peter Gojowczyk.
Luxembourg's Gilles Muller, who is seeded 16th, pushed himself to the limit before posting a 7-5, 6-7 (7), 4-6, 6-3, 9-7 victory over Czech Lukas Rosol in three hours, 37 minutes.
Muller, who won his first grass-court title at the Ricoh Open in 's-Hertogenbosch last month, recorded 45 aces and 95 winners to advance to face Brit Aljaz Bedene, who beat Bosnian Damir Dzumhur 6-3, 3-6, 6-3, 6-3.
American Sam Querrey fired 32 aces and won all 11 of his points at the net to beat Nikoloz Basilashvili and move into the third round.
The 24th-seeded Querrey, who upset Novak Djokovic in last year's third round, defeated Basilashvili, from the country of Georgia, 6-4, 4-6, 6-3, 6-3 at the All England Club in London in one hour and 51 minutes.
France's Jo-Wilfried Tsonga, the No. 12 seed, capitalized on lapses from qualifier Simone Bolelli of Italy in a 6-1, 7-5, 6-2 victory over one hour, 55 minutes.
"Today, it was good because I won," Tsonga said afterward. "That's the most important thing, I think, to win. I think I can play even better. And I have to if I want to do better in this tournament."
It has been 71 years since a Frenchman lifted the title at Wimbledon when Yvon Petra beat Australia's Geoff Brown in five sets for the 1946 title.
Tsonga reached the Wimbledon semifinals in 2011 (lost to Djokovic) and in 2012 (lost to Andy Murray). Tsonga will next play Querrey.
"Sam is playing well -- that's not a new story," Tsonga said. "He's playing well on this surface. He always has been very dangerous on this surface. So for me it's a really serious match. I hope I will be able to play good tennis and be even more focused than today."
Belgian qualifier Ruben Bemelmans continued his run of quality wins this week, defeating Russian Daniil Medvedev 6-4, 6-2, 3-6, 2-6, 6-3.
The win puts the 29-year-old Bemelmans into the third round at Wimbledon for the first time in his career. He defeated Tommy Haas in the opening round, while Medvedev caused the upset of the tournament thus far by taking out No. 5 seed Stan Wawrinka on Monday.
Medvedev didn't take too kindly to losing on Wednesday, as he grabbed his wallet and pulled out some coins before tossing them at the foot of the umpire's chair. This action came moments after he shook hands with chair umpire Mariana Alves.
"I was disappointed with the result of the match," Medvedev said. "It was frustrating after a big win I had. All the match was not going well for me. So I was just very (disappointed). In the heat of the moment, I did a bad thing. I apologize for this."
In a first-round match carried over from Tuesday, Italian No. 32 seed Paolo Lorenzi broke an 11-match grass-court losing streak by beating Horacio Zeballos of Argentina 7-6 (3), 4-6, 7-6 (8), 7-5.