Third-seeded Murray had the easiest path to victory on New Year's Eve, barely breaking a sweat during his 6-0, 6-0 win over 2,129th-ranked Qatari wild-card recipient Mousa Shanan Zayed.
"Yeah, it was pretty easy," Murray said. "It's kind of a tough situation. It's not something you're really looking forward to, but you just have to try and play and concentrate.
"In terms of feeling sorry for him, not really. I mean, after the match but not during it."
The match took all of 37 minutes and Murray hit the practice courts later for a little extra court time.
Murray won all but 17 points in the match, and won all 20 points when his first serve went in.
"It's fairly rare but you see it once, maybe twice in a season," Murray said of the service statistics. "Definitely for individual sets. Maybe not always for an entire match."
Zayed has only played two tour-level matches, losing the other match to Gael Monfils in the first round at last year's event in Doha.
Top-ranked Nadal breezed through the opening set, but was tested in the second set by Lukas Rosol before securing a 6-2, 7-6 (7) win on his fifth match point of the tiebreaker.
Nadal's only previous match against Rosol was a five-set loss in the second round at Wimbledon in 2012. After that match, Nadal took seven months off the tour with a knee injury.
"I was a little bit nervous," Nadal said, "I didn't have a great memory of the last match playing against him."
Second-seeded David Ferrer had a 6-3, 5-7, 6-3 win over Alexandr Dolgopolov of the Ukraine, while defending champion Richard Gasquet advanced with a 7-5, 6-1 win over Egyptian wild-card recipient Karim Hossam.