He reached the last four after top seed Jannik Sinner withdrew with a hip injury before their quarter-final tie, while the 23-year-old was a set up when Jakub Mensik had to retire hurt in the last 32.
Injuries have been an unwanted theme of the tournament with Lehecka, who beat Rafael Nadal on the way to his first ATP Masters 1000 semi-final, the opponent when third seed Daniil Medvedev pulled out a set into their quarter-final match on Thursday.
But while Auger-Aliassime will go into Sunday’s final having only played half a set since Tuesday, Rublev has had a more conventional route to the final.
He battled past second seed Carlos Alcaraz in three sets in the quarter-final before his straight-set win over Fritz in the semis.
Twelfth seed Fritz broke in the opening game of the match but Rublev hit straight back before breaking to love to clinch the first set.
Rublev had to ward off two break points at the start of the second and, having done so, secured the decisive break midway through the set.