The No3 seed received an ear-splitting ovation as he walked onto court and little over two hours later completed a 6-1, 6-4, 7-5 win.
Murray said: “One of the things [coach Amelie Mauresmo] said was she tried to take in the atmosphere and the experience of walking out on the court as the defending champion. You never know if you’ll get the chance to do it again. To come to the court and get that reception, it was very nice.”
Murray had never lost a first-round match at the All England Club and hit the ground running with a nerve-settling break of serve at the first opportunity, before closing out the opening set in just 29 minutes.
The 27-year-old gobbled up the second of two break points to take a 2-1 lead in the second set and never looked back. Goffin applied pressure for the first time as he settled in the third set but Murray showed all the grit of a champion to save break points when trailing 2-1, then sealed a second-round meeting with 6ft 4in Slovenian Blaz Rola with an ace.
He added: “It does help if you can get ahead early. There weren’t any moments where I felt like I was mistiming balls. I played very well.”
Flying the flag for Britain in the ladies’ draw was 24-year-old wildcard Naomi Broady, who upset Timea Babos on Court 16 to book a second-round spot.
Broady, ranked 164th in the world, receives no funding from the Lawn Tennis Association due to a long-standing row, and even considered quitting the game to become an au pair recently such is the extent of her money worries, but will earn at least £43,000 in prize money following her victory.
Sam Stosur and Sloane Stephens, seeded 17th and 18th respectively, lost their first-round ties, as did 18th seed Fernando Verdasco.
Centre Court (from 1pm)
Martin Klizan (SVK) v
Rafael Nadal (ESP) 
Serena Williams (USA)  v
Anna Tatishvili (USA)
Court One (from 1pm)
Samantha Murray (GBR) v
Maria Sharapova (RUS)