- 1,612
- 9
- 38
Murray's victory, which spanned over three hours, means he stays unbeaten this season in matches that have gone to a deciding set.
So far this year, Murray is 5-0 in best-of-three-set matches to go the duration, along with 2-0 in best-of-five matches that go to five. He is 0-3 in contests that conclude earlier.
Dan Evans and Jack Draper make up the British contingent in the men's draw and face each other in their next ties and the victor will face either Murray or Busta in the third round.
In the women's draw, Emma Raducanu returned to the court for the first time since her second-round exit to Coco Gauff at the Australian Open.
She marked her injury comeback with a 6-2 6-3 win over Danka Kovinic in the opening round of the BNP Paribas Open in Indian Wells.
Raducanu's participation in her first match since losing to Coco Gauff in the second round of the Australian Open in January had been in doubt after she revealed the wrist problem she was troubled by last season had returned.
But the British No 1, who withdrew from last week's event in Texas and an exhibition tournament earlier this week, delivered a composed performance, despite clearly not being at 100 per cent, to progress to the next stage.