The 27-year-old Belarusian is a three-time Grand Slam champion but has never been beyond the semi-finals at the All England Club.
She is looking to ease the pain of losing in the finals of the Australian Open and the French Open this year.
Sabalenka broke Branstine twice in a one-sided first set as the Canadian struggled with her serve.
Branstine was a tougher proposition in the second set, winning the first game to love on her own serve, but missed a chance to break in the next game.
The 24-year-old was playing her first Grand Slam main-draw match but enjoyed significant wins over French Open semi-finalist Lois Boisson and Bianca Andreescu in qualifying.
The match were locked at 5-5 in the second set before Sabalenka broke in the 11th game and served out the victory to set up a meeting with New Zealand’s Lulu Sun or Czech player Marie Bouzkova. (AFP)