While Rafael Nadal was suffering his second shock exit at the All England Club in two years, Murray was doing just what he needed in a 6-4 6-3 6-2 victory that took an hour and 52 minutes.
Murray became a little sloppy after a fine start but once he had the first set in the bag he did not look back.
"I thought it was a good match and it was a good start for me. He played some solid tennis especially the first two sets and then the third set I started to play better," Murray told the BBC.
"It was a tough start for me, he is a very good grass player. I was ready and to win in three sets was a good start. There's always nerves at the start of a grand slam and I'm glad to get it out of the way and hopefully I can improve as it goes on."
Playing his first match on Wimbledon's Centre Court since the Olympic final, the British number one faced a player he beat in straight sets on his way to the title at Queen's Club two weeks ago.
Murray has been talked up even more than usual following his glorious summer last year.
And yesterday Roger Federer, the man Murray beat so comprehensively to win Olympic gold between losing the Wimbledon final and landing the US Open title, picked out the second seed as the player he sees as his biggest title threat.
Murray has talked in the build-up of feeling less pressure because of what he has already achieved, but he began slightly nervously and had to save a break point in the opening game.
Clearing that hurdle seemed to settle Murray down and he broke for 3-1. Looking completely comfortable on the grass, he then had two points for a 5-1 lead but could not take either.
Becker is definitely not the most talented player of that name to come out of Germany but he was the beneficiary of a sloppy game from Murray, who double-faulted to drop his serve.
The home favourite had lost his surety but it seemed only a matter of time before he upped his level again and so it proved as Murray forced two set points, taking the second and the set when Darcis scrambled a backhand wide.
Murray was sporting the name of the Royal Marsden Cancer Charity, where his good friend and British Davis Cup team-mate Ross Hutchins has been receiving chemotherapy, on his sleeve.
Hutchins was watching from the Royal Box but Murray was still having a few struggles and, like in the first set, Becker had chances in the opening game but could not take them.
The top players always try to peak for the second week, and Murray is rarely at top form in his first-round matches at the slams.
It was the same in this case, but Becker's resistance cracked in the eighth game, a wild backhand giving Murray a 5-3 lead, and the set soon followed.
It was routine for Murray, and the greatest reaction from the crowd came every time the score in Nadal's match flashed up on the scoreboard.
There were no first-game wobbles from Murray in the third set as he began with a break of the Becker serve, and it was just really a question of how long it would take him to wrap it up.
Becker battled on gamely, saving two break points in the seventh game but not a third, a shanked forehand leaving Murray serving for the match.
The Scot's forehand had been particularly impressive and another winner, his 38th of the match, sent him through to a second-round clash against either fellow Briton James Ward or Lu Yen-hsun.