The day's main draw featured 2013 Wimbledon champ Murray against controversial Australian Nick Kyrgios in a late matchup.
Murray was able to fend of his friend Kyrgios with surprising ease, winning 7-5 6-1 6-4 in a speedy one hour and forty-two minutes.
Kyrgios, who appeared distracted throughout the contest, is now 0-5 against Murray in his career.
World No. 2 Murray recently retained coach Ivan Lendl, who was by his side when he won his only two grand slams to date (the other being the 2012 U.S. Open).
By contrast, Kyrgios is currently without a coach -- a move generally favored only by lower ranked players who cannot afford them.
It may well be money worth spending, however. Kyrgios's game was littered with unforced errors -- 19 to Murray's 6 -- some of them a result of unnecessary trick shots, including one which allowed Murray to go 3-1 up in the second set.
After giving up yet another break to go down 3-1 in the third set, Kyrgios did not even bother to sit down between changeovers
"Nick lost his focus a bit in the middle part of the (second) set so that made it a little bit easier," Murray told the BBC after the match. "I was able to dictate a part of the rallies and managed to get up a break and that helped."
The 21-year-old prepared for his Centre Court match by watching compatriot Lleyton Hewitt play doubles -- a move that was criticized by commentators.
"He's got to look in the mirror if he wants to be a top player and win slams now," three-time Wimbledon winner John McEnroe said of Kyrgios on the BBC after the match. "You're not going to make it on the top with that kind of effort."
Murray is now the favorite to win his second Wimbledon, given that No. 1 seed Novak Djokovic didn't get past the first week.
So far neither Murray nor Roger Federer has given up a set during this Wimbledon campaign, and the two are poised to meet in the finals in a rematch of their 2012 four set classic. It was also the last time Federer won at the All England Club.
Murray faces Jo Wilfried Tsonga next, who was delivered a break when Frenchman Richard Gasquet withdrew with an early injury. Tsonga was coming off an exhausting match against John Isner, which finished 19-17 in the fifth set on Saturday.
Federer gunning for record
Meanwhile, Roger Federer
sailed through to the quarterfinals after a straight sets victory over world No. 29 Steve Johnson in Monday's early match-up on Centre Court.
On a mission to build on his current record of seven Wimbledon titles, which he shares with Pete Sampras, Federer never looked rattled by his 26-year-old opponent as he sailed through 6-2 6-3 7-5 in just 97 minutes.
The world No. 3 had his forehand working, hitting 35 winners while covering slightly less distance than Johnson, who was in uncharted territory -- both by reaching the fourth round of a grand slam and by facing Federer for the first time.
Johnson showed signs of life at 5-5 in the third set, but failed to dispute an out call -- which was clearly in bounds -- that may have prevented Federer from breaking him to serve for the match.
Perhaps Johnson was distracted by Federer's side of the box, where he had former coach Stefan Edberg and Vogue editor Anna Wintour cheering him on, along with his usual entourage of family members.
But the underdog had support too, with cries of "C'mon Stevie Wonder!" emanating from the crowd early, though it just wasn't enough.
In a typically frustrating sequence down 3-2 in the first set, Johnson raced to a 30-0 lead with a stunning 89 miles-per-hour forehand winner that nipped the far corner behind the advancing Federer -- only to come undone with a net return on the next point, one of his 21 unforced errors of the match (Federer had just 13.)
Fed broke to go up 4-2 and it was smooth sailing from there on. He finished the match with a clinical second serve ace.
"I was very happy how I played, and I didn't think it was as easy as it maybe looked," Federer told the BBC after the match. "Steve was coming into the match with a lot of confidence."
Federer's progress has been straightforward so far, including a win over 772-ranked Marcus Willis in the second round.
"I never thought that I would win the first four matches in straight sets. The matches might be tough, but the rest in between is nice," he added. "For professional athletes that's huge."
Marin Cilic, the world No. 13 from Croatia, will face Federer in the quarterfinals.
The Croatian advanced against world No. 6 Kei Nishikori, who was also forced to withdraw due to injury. The former U.S. Open finalist from Japan suffered back problems from the onset, winning just seven points in the first set before finally conceding the match down 4-1 in the second.
Serena on pace
Also on Centre Court, six-time Wimbledon winner Serena Williams defeated world No. 14 Svetlana Kuznetsova to march into the ladies' quarterfinals.
A rain delay at 5-5 in the first set galvanized the flustered world No. 1, who suffered two breaks of serve to that point.
Kuznetsova seized a break point at 4-4, rushing to the net with with a backhand winner that wrong-footed a falling Williams. The defending champion remarked to the chair umpire that the drizzle which descended upon Centre Court had her concerned for her safety.
Serena then buried her head in a towel during the changeover, clearly frustrated that she had allowed her challenger to come back from a break point down early. Nevertheless, Williams broke back to 5-5 before again voicing her concern about dampness .
This time the chair umpire agreed, allowing the opponents to retreat to the locker room while the retractable roof was closed.
Serena would not lose another game in the entire match.
Velocity in her serve improved, while she knocked in a flurry of winners to take the next two games and the first set 7-5.
She then rolled 6-0 in the second set to close out the match.
Sister Venus Williams also advanced in straight sets, beating Spaniard Carla Suarez Navarro 7-6 6-4. Venus, the No. 8 seed and five-time Wimbledon champion, is on the opposite side of the draw to her sister, and the two could meet in the finals for a fifth time.