Paire was business-like in his 6-3 7-5 dismissal of Prajnesh Gunneswaran on Tuesday, crushing his 14th ace on match point to avenge his loss to the 29-year-old at Indian Wells in March.
Paire's win sets the stage for a third round showdown with fellow Frenchman Ugo Humbert, who was a 3-6 6-3 6-2 winner over American Bjorn Fratangelo at the ATP 250 event.
Second seed Shapovalov looked sharp en route to 6-2 6-4 victory over American Tennys Sandgren, who had defeated three-time Grand Slam champion Andy Murray the night before.
Next up for hard-hitting Canadian Shapovalov is a meeting with Serbian teenager Miomir Kecmanovic in the round of 16 on Wednesday.
Lee Duck-hee, who on Monday became the first deaf player to win a match in the main draw of an ATP event, fell to rising Polish Hubert Hurkacz 4-6 6-0 6-3.
Russian Andrey Rublev, fresh off his impressive win over Roger Federer at the Cincinnati Masters, was forced to play two matches on Tuesday due to rain on Monday but won both and will meet big-serving American Sam Querrey.
Italian Lorenzo Sonego, Serbian Filip Krajinovic, Spanish veteran Feliciano Lopez and young Americans Frances Tiafoe and Steve Johnson were among those who also booked their tickets to the third round on Tuesday.