World number 33 Raducanu proved too strong for 32nd seed Stearns and has now won all three meetings against her.
An early break put her in control of the first set before she took her sixth set point on her opponent’s serve.
Raducanu trailed 4-2 after falling a break down in the second, but produced an impressive finish with a run of four consecutive games to clinch victory.
“I’m really happy with how I came through in that match,” Raducanu said.
“I kind of lost my focus at some moments in the second set and she took advantage, but very happy that I came through against a top opponent and happy to extend my stay in Montreal.
“I just want to say thank you [to supporters], I saw the Union Jack in clutch moments and I was actually born in Canada, so to me it means so much to do well here.”
