Earlier this month Evans bemoaned his failure to get to grips with the surface after Great Britain lost their Davis Cup quarter-final to France.
But he finally rose to the occasion against Thiago Monteiro of Brazil, storming through a final set tie-break to triumph 6-7 (4) 6-2 7-6 (2).
When Evans dropped the first set he looked set to fall to another defeat against the world number 80, who holds a win over Jo-Wilfried Tsonga on the surface.
But Evans rallied to break Monteiro three times in the second set, and won the first five points of the ensuing tie-break to set up a second round clash with Mischa Zverev.
Fellow Briton Kyle Edmund continued his own fine form on the surface as he brushed aside Frenchman Jeremy Chardy 6-3 6-4 to reach the second round.
The British number two, who pushed Rafael Nadal to three sets in Monte Carlo last week, will now head into a second round match against Dominic Thiem.
Edmund seized his solitary break point opportunity in the first set to nudge into the lead and one further break in the second was enough to complete victory.
Additional reporting by the Press Association.