Barty could have re-taken the top ranking she lost last week to Japan's Naomi Osaka had she reached the final.
The shutdown triumph by the 34-year-old double Grand Slam winner leaves injured Osaka atop the rankings with the US Open starting a week from Monday.
Kuznetsova will play for the title on Sunday against the winner of a later semi-final between Americans Sofia Kenin and Madison Keys.
In later ATP semi-finals, top-ranked Novak Djokovic of Serbia faces Russia's Daniil Medvedev and France's Richard Gasquet will meet Belgium's David Goffin.
Barty, who had rallied from a set down to win her previous two matches, was off the boil against Kuznetsova, who is back on form after several seasons of injuries, including a wrist problem.