Konta battled back from a set down to move to the second round in Montreal with a 6-7 (6/8) 6-1 6-2 victory over Jelena Ostapenko.
The world number 43 began with plenty of promise, breaking her Latvian opponent twice to race into a 3-0 lead in just nine minutes, but Ostapenko battled back and edged the tie-break.
The next set followed a similar pattern to the first with Konta again winning the opening three games.
Ostapenko was unable to mount a fightback and the British player's dominance continued in the final set, securing three breaks before successfully serving for the match to complete an impressive comeback.
Konta will play Azarenka in the second round after the Belorussian routed Kristina Mladenovic 6-0 6-1.
The two-time grand slam winner, 29, who had a son in December 2016, defeated her French opponent, 25, in under 56 minutes.
Breaking each of Mladenovic's serves in the first set to deny her a point, Azarenka only let one past in the second set.
The winner told WTA after the game: "It's very difficult for women when they become mothers. Your body changes, and so does your mind, and you have different priorities."
Five-time grand slam winner Sharapova set up a second-round clash with fellow Russian Daria Kasatkina, the number 12 seed, with a formidable performance over Sesil Karatantcheva.
Now ranked 229 by the WTA, Karatantcheva was no match for Sharapova, currently at 22, who won 6-1 6-2 in one hour and 20 minutes.
In other matches Anastasia Pavlyuchenkova set up a second-round clash with world number one Simona Halep after beating Christina McHale 6-3 6-2.
Meanwhile number six seed Caroline Garcia came from a set down to beat Magdalena Rybarikova 4-6 6-1 6-3 in the second round.
Petra Kvitova, the number eight seed, beat Anett Kontaveit 6-3 6-4 in the second round and number 10 seed Julia Goerges progressed to the third round after beating Lucie Safarova 2-6 6-4 6-3.
On Wednesday Sorana Cirstea will play number 13 seed Venus Williams in the second round after beating Monica Niculescu 3-6 6-4 6-4.
Number four seed Angelique Kerber will play Alize Coronet after the Frenchwoman beat Tatjana Maria 4-6 6-1 6-3.
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