The 36-year-old three-time Grand Slam winner disclosed at the Dubai Tennis Championships last month that he does not intend to “play much past this summer”.
Murray easily defeated the Belgian qualifier 6-3 6-2 in his first match back since then.
But in California, Jack Draper and Katie Boulter of Britain lost in the first round.
After only winning two of his eight matches before to Indian Wells, Murray has struggled for victories in recent months, raising concerns about his future.
Nonetheless, the former world number one appeared to be in fine form as he defeated Goffin in a 34-minute opening set by serving two aces.
