Murry had to overcome a slow start against Australia's Matthew Ebden, losing the first set before moving through the gears and turning the match around decisively. He won 12 out of 13 games to kick-start his title defence with a 3-6, 6-0, 6-1 win in an hour and 37 minutes.
Although Murray's split with Lendl was amicable, the British No 1 admitted it was a difficult time. "It was very different without him, it's been a hard few days," Murray said of the man who helped him break his Grand Slam duck at the 2012 US Open before adding last year's Wimbledon title, having also won Olympic gold at London 2012.
"He's been a big part of my career and to not have him around is going to be tough, but I need to get on with it and try to get back to playing my best tennis."
Murray, seeded sixth in Miami, gave himself an uphill task at the start of his title defence when Ebden won the opening set 6-3 in 39 minutes. Murray had to make a good start in the second set and he did, breaking at the first attempt. He faced two break points in the next game after sending a forehand long, but saved both and consolidated his break.
Another followed as the Wimbledon champion began to benefit from a more aggressive approach as he took balls from well inside the baseline.
He went 5-0 up and won the set when he broke again in the next, helped by a net cord on set point.
Murray was broken in the opening game of the decider which sent the Scot into a towel-tossing rage as he berated himself. The chastising had the desired result as he instantly broke back to get on level terms and raced through the next five games to clinch a convincing victory.
Murray said: "You do what you do to win. It's not always about how you play or how calm you are on court, it's about winning the match. That's what matters."
Murray will look to extend his perfect record against Feliciano Lopez to 9-0 when they meet in the third round. The No 32 seed ousted young gun Jiri Vesely 6-2, 7-6(3) in 92 minutes.
Australian Open champion Stan Wawrinka survived a rollercoaster start to his campaign with a 6-0, 3-6, 6-3 win over Spain's Daniel Gimeno-Traver. The third- seeded Swiss, playing just his second event since his milestone win in Melbourne, blasted through the opening set in just 18 minutes, but then made tough work of the remainder of his centre court clash, needing nearly an hour-and-a-half to finally tame the Spaniard.
The victory pushed Wawrinka's record to a near perfect 14-1, a run that includes a pair of titles.
Seventh-seeded Czech Tomas Berdych joined Wawrinka in the third round by dispatching Frenchman Stephane Robert 7-6(5), 6-1 while big-hitting Croatian Marin Cilic, the 25th seed, was shown the exit by France's Edouard Roger-Vasselin 6-2, 7-6.
In the women's event, defending champion Serena Williams survived an epic battle to edge past France's Caroline Garcia in three sets in a match lasting more than two-and-a-half hours. Williams took the opening set 6-4, but lost the second by the same score, gifting her opponent two set points with a sixth double fault of the contest.
An early break in the decider looked to have eased Williams' passage to the next round, but Garcia saved five break points before Williams eventually sealed a hard-fought 6-4, 4-6, 6-4 win.
Meanwhile, Juan Martin del Potro will undergo a second wrist operation in four years tomorrow and miss the rest of the season. Del Potro will have surgery on his left wrist which he uses for his backhand, having had an operation on his right wrist in May 2010.