Murray, a Scotsman ranked No. 2 in the world, took the first set 6-2 but Capdeville, a Chilean ranked 87th, grabbed the second 6-3. Murray responded by winning the next two sets 6-0, 6-2.
In the up-and-down effort, Murray overcame 22 errors in the first two sets, then recorded only eight errors in the final two sets with 15 service aces and 44 winners, but three double-faults.
"Basically, I played three good sets and one bad one," Murray said after continuing his quest for a first career grand slam tournament victory.
He lost last year's final to five-time defending champion Roger Federer, but could become the world's top player if he wins this event.
Elsewhere, sixth-seeded Juan Martin del Potro, No. 7 Jo-Wilfried Tsonga and No. 9 Gilles Simon also were second-round winners and 17th seed Tomas Berdych topped Horacio Zeballos 6-3, 6-7 (3-7), 7-6 (7-2), 6-2.
Celebrity Families of 2014 [PHOTOS]