Britain's Dan Evans fell at the first hurdle in the Italian Open on Monday, but Stan Wawrinka posted his first victory on the ATP Tour for over a year.
Despite posting seven aces and only one double fault compared to Basilashvili's five, Evans was broken four times to slump to a 7-6 [7-2] 6-2 defeat on the clay.
The 31-year-old is still waiting for his first appearance in the second round of the Masters 1000 event, having now suffered five consecutive first-round exits on Italian turf.
However, the feel-good story in the men's tournament belonged to Wawrinka, who was previously without a win on the ATP Tour for 15 months after undergoing foot surgery.
A wild forehand on serve for Opelka handed Wawrinka the victory, and he will now face Laslo Djere in the second round of the tournament.
Denis Shapovalov also powered past home favourite Lorenzo Sonego in three sets despite a verbal outburst towards the crowd and argument with the umpire, while Karen Khachanov and Alejandro Davidovich Fokina have also advanced.
However, Naomi Osaka has announced her withdrawal from the Italian Open due to injury, with the three-time Grand Slam champion taking extra care before the start of the French Open.
"Unfortunately I'm going to have to withdraw from Rome as the injury which I picked up last week in Madrid hasn't healed yet. It's an Achilles injury, so I need to be careful especially in advance of Roland Garros," Osaka said in a statement.
Tuesday will see Emma Raducanu take to the court for her first-round match with Bianca Andreescu, while Madrid Open champion Ons Jabeur, Iga Swiatek, Rafael Nadal and Novak Djokovic will also be in action.