Former world number one Murray, who won his first Wimbledon title in 2013 before adding a second three years later, came through 6-3, 6-0, 6-1.
Now ranked at 40, and playing with a metal hip, the 36-year-old had too much power and finesse for wildcard Peniston, the world number 268.
"It's amazing to be back on Centre Court again," said Murray.
"I started off quite nervously, I was a little bit tentative but once I got a break I played some good stuff. There were good signs."
He added: "It's a long time since I felt this good coming into an event as the last few years have been challenging.
"Hopefully I am fit and ready enough for a good run."
Once Murray broke for a 4-2 lead in the first set under the roof of Centre Court at a rain-lashed All England Club, there was little doubt over the outcome.
He swept through the second set on the back of three breaks of serve and was 2-0 ahead in the third before Peniston stopped the bleeding.
It was too little, too late for Peniston as Murray broke again for 4-1 on his way to securing his 199th Grand Slam match win.
Murray faces a tougher test in the second round where he will play fifth-ranked Stefanos Tsitsipas or former US Open winner Dominic Thiem.