"If you can finish matches as quickly as possible, it definitely helps in the long run," Murray said.
Williams overcame a slow start to beat Japan's Kurumi Nara 7-6 (4), 6-1 to get past the second round of a major for only the second time in her last 10 Grand Slam tournaments.
"It's definitely a step in the right direction," Williams said. "The thing that I just have to really work on is being on tour consistently and playing tournaments."
Next up for Williams is a third-round clash with 2011 champion Petra Kvitova, the Czech lefthander who downed Mona Barthel of Germany 6-2, 6-0.
"I think we both play similar games, really go for it," Williams said. "She's one of the kind of players who can get kind of hot against me."
For Murray, it was one of the most emphatic wins of his career. He never previously had dropped fewer than six games in a match at Wimbledon, and it was his most one-sided victory at a Grand Slam since losing just one game to Alberto Martin at the Australian Open in 2007.
The 23-year-old Rola, who won the 2013 NCAA singles championship for Ohio State, was playing in Wimbledon for the first time. He has been playing primarily on the lower-tier Challenger Circuit and looked out of his league against Murray on Court 1.
Murray broke eight times, saved the three break points against him and had only 13 unforced errors.
"I played well today," Murray said. "This is the first year he's played on grass. He just came out of college and he's broken into the top 100. It was tough for him today. He doesn't have much grass court experience, but I think he'll keep improving."
The 30th-seeded Williams won six straight points in the tiebreaker after being down 1-4 and ran off six straight games in the second set to beat 41st-ranked Nara on Court 3 at the All England Club.
"In the tiebreaker, that's when it comes down to who's going to be more consistent and more aggressive," Williams said. "In the beginning, she was. But thankfully I was able to turn it around."
Williams, winner of seven Grand Slam titles, lost in the first round in her last appearance at Wimbledon in 2012. The only other time she has made it past the second round in her last 10 Grand Slams was at the 2013 Australian Open. She hasn't reached the fourth round at a major since Wimbledon in 2011.
The 6-foot-1 Williams towered over Nara, the shortest player in the women's top 100 at 5-1.
The American served seven aces and had 43 winners. Nara had only five unforced errors but just 16 winners.
Nara took a medical timeout at the end of the first set and received treatment from the trainer on her upper left leg during the second set. She said it was nothing serious.