Top seed Sinner defeated the French qualifier 6-4 7-6 (7-4) after an almost three-hour rain interruption on Wednesday.
The Italian struggled to find his rhythm, failing to serve it out at 6-5 but sealed the tiebreak with back-to-back aces for his 24th consecutive hard-court victory.
Mannarino "is a very tough opponent. Very different from other opponents, not only because he is a lefty but how he hits the ball. It is very low," the 23-year-old defending champion said.
"I just tried to serve well and tried to see what I could do in the return games."
Sinner will face 23rd seed Felix Auger-Aliassime next, in what will be the four-time grand slam winner's fifth quarter-final of 2025, after the Canadian enjoyed a 6-4 6-3 win over France's Benjamin Bonzi.
Ben Shelton, whose match was also halted after the first set, advanced to the round of 16 with a 7-6 (7-3) 6-3 victory over Roberto Bautista Agut. The American fifth seed will next face Czech Jiri Lehecka.
Alexander Zverev completed a 6-4 6-4 win over Brandon Nakashima after the match was suspended overnight when he was leading 5-4 in the second set.
The German third seed is set to return to the court later on Wednesday, aiming to avenge last week's Toronto semi-final loss to Russian Karen Khachanov.
Earlier, seventh seed Holger Rune advanced after home favourite Frances Tiafoe was forced to retire with a back injury.
Spanish second seed Carlos Alcaraz booked his 18th Masters 1000 quarter-final by beating Italian Luca Nardi 6-1 6-4.
The five-times major winner, into the last eight in Cincinnati for the third time, has now won 36 of his last 38 matches.
"This match was the best so far for me in this tournament," Alcaraz said.
"I'm really happy with the way I felt the ball today and the way that I moved. I got used to the conditions, the humidity and heat. I'm happy to get through."
Alcaraz will next face Russian ninth seed Andrey Rublev, who beat Argentine Francisco Comesana 6-2 6-3.
German third seed Alexander Zverev, who completed a 6-4 6-4 win over American Brandon Nakashima after the match was suspended overnight when he was leading 5-4 in the second set, progressed to the quarters after Russian Karen Khachanov was forced to retire due to injury while trailing 7-5 3-0.
French qualifier Terence Atmane earned the biggest win of his career by stunning American fourth seed Fritz 3-6 7-5 6-3, earning his first Masters 1000 quarter-final berth.
Atmane will meet Danish seventh seed Holger Rune, who advanced after American 10th seed Frances Tiafoe retired due to a back injury.
