The powerful Frenchman who missed seven months last season due to knee surgery and rehab, carried over his momentum from a weekend title in Montpellier, where he beat countryman Pierre-Hugues Herbert.
Tsonga, ranked 140th as he fights back towards the elite, spent 66 minutes in dispatching qualifier Fabbiano.
Tsonga, 33, has been steadily lifting his ATP ranking from its low point of 210 and is playing Rotterdam for the first time since winning the title two years ago.
The Frenchman, one of four former Rotterdam champions on court Wednesday, was pleased with his showing as he won his 10th match from 12 played since the start of the season.
"I played well in the first set and kept my level in the second," he said. "My opponent raised in the second but I held on.
"I've been working hard and trying to spend my time on court in a good way,"
Tsonga next plays Dutch wild card Tallon Griekspoor, who knocked out second seed Karen Khachanov on Tuesday.
The No 211 outsider will be the subject of intensive YouTube viewing sessions from the Tsonga team over the next 24 hours.
"I really don't know about him, but we will work on it. I'm playing good tennis and that's the most important thing for me," Tsonga said.
"I'm happy to win matches and titles - like last week. I know my comeback is still under construction, though."
Russian fifth seed Daniil Medvedev emerged a winner in his opening match of the week, beating France's Jeremy Chardy 7-6 (7/2), 6-2. Hungarian Marton Fucsovics put out 2016 Rotterdam champion Martin Klizan 7-6 (7/4), 6-4.
Medvedev, who turned 22 on Tuesday, came to the Dutch port city with a weekend title to hand after winning his fourth career ATP trophy in Sofia.
With a 12-2 record so far in 2019, he is off to a personal-best season start heading into a match with Fernando Verdasco.
Results from the ATP tournament in Rotterdam on Wednesday (x indicates seeding):
Daniil Medvedev (RUS x5) bt Jeremy Chardy (FRA) 7-6 (7/2), 6-2
Marton Fucsovics (HUN) bt Martin Klizan (SVK) 7-6 (7/4), 6-4
Jo-Wilfried Tsonga (FRA) bt Thomas Fabbiano (ITA) 6-1, 6-4