The 25-year-old, who will take over top spot from Poland's Iga Swiatek with victory at the Paris grand slam, did not have an easy start with qualifier Shymanovich, ranked 214th, matching her power with every groundstroke.
Shymanovich started moving her opponent around, playing the angles and forcing her to the net with audacious drop shots as she tried to stop Sabalenka imposing her own rhythm on the match.
The second seed wasted two set points at 6-5 but bagged the set on her third opportunity, chasing down yet another drop shot from her opponent.
She took a two-game lead at the start of the second set but had to fight tooth and nail for every single point before sealing victory on her second match point.
French Open debutant Peyton Stearns produced the biggest win of her career by defeating former champion Jelena Ostapenko to reach the third round at Roland Garros.
Stearns, a former player at the University of Texas, only turned professional in June last year.
Ostapenko won the 2017 French Open but has since failed to advance past the third round. The 17th-seeded Latvian dropped her serve five times against Stearns and hit 28 unforced errors in her 6-3 1-6 6-2 loss.
The 21-year-old Stearns has been climbing the WTA rankings and entered the French Open at No.69 on the back of an encouraging clay-court campaign.
Third-seeded Jessica Pegula also advanced after Camila Giorgi retired due to injury. The American led 6-2 when her Italian rival threw in the towel.
Only hours after husband Gael Monfils won a five-set thriller in Tuesday night's session, Elina Svitolina rallied past qualifier Storm Hunter 2-6 6-3 6-1.
