Sharapova struggled at times with her accuracy but unleashed some massive serves and played stout defence at key moments on her return to the tournament after a five year absence.
Fellow tournament wild card Riske looked poised to send the match to a third set when she was serving on 5-3 and 15-0 in the second set but Sharapova upped her game to force a tiebreaker.
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Former world number one and five-time Grand Slam champion Sharapova prevailed on her fourth match point to set up the meeting with top seeded Barty.
Barty defeated Sharapova in the fourth round of the Australian Open in January and both will be looking to sharpen their games ahead of the U.S. Open later this month.
Another former world number one, Caroline Wozniacki, fell to rising Ukrainian teenager Dayana Yastremska 6-4 6-4 under the lights to close out the day's action.
The unseeded Dane had her opportunities but converted just four of her 15 break point chances against Yastremska, who was making her Cincinnati debut.
Svetlana Kuznetsova upset 11th seeded Anastasija Sevastova 7-6(3) 6-7(4) 6-4 in their first-round battle to set up a second round clash with Yastremska.
KONTA CRASHES OUT, WILLIAMS WINS
British number one Johanna Konta lost in the first round of the Cincinnati Masters to qualifier Rebecca Peterson in a topsy-turvy match.
Peterson served well to take the match 6-3, 3-6, 7-5.
Former world number one Venus Williams moved through the first round of the Cincinnati Masters when she defeated compatriot Lauren Davis in straight sets on Monday.
Wild card Williams won 7-5 6-2 on centre court as she maintained her streak of never having lost a set to Davis, having beaten her four times.
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