The five-time Grand Slam champion has not played since the end of January after taking time out to recover from a shoulder injury, but edged a tight opening set against Kuzmova before strolling through the second.
Victory on the grass will come as a timely boost to morale for Sharapova, with the start of Wimbledon now less than two weeks away.
"It's my first win in about three or four months," Sharapova said afterwards.
"It's great to be here in Mallorca. What a great place to train and have a warm-up tournament. It's been amazing for all of us here, and it's just been nice to experience it for the first time."
Angelique Kerber now awaits Sharapova in round two after the top-seeded German defeated Belgium's Ysaline Bonaventure 7-5, 4-6, 6-2.
Kerber has struggled for form herself this year but is likely to offer a sterner test than Kuzmova, the Slovak ranked 46th in the world and who is still only 21.
Sharapova's own ranking has dipped to 86 during her absence, meaning the Russian needed a wildcard to enter the draw in Mallorca, her fourth tournament this year.
A tense first-set tie-break required Sharapova to save two set points before clinching the frame and Kuzmova never recovered, a limp second set ending with a half-volley dropped into the net.
Earlier, another former major champion crashed out as France's Caroline Garcia came from behind to beat Victoria Azarenka 1-6, 6-4, 7-5.
Garcia maintained momentum with an impressive victory over the Belarusian, fresh from winning her first title of the year and seventh of her career at the Nottingham Open on Sunday.
The world number 28 will now face Spain's Paula Badosa Gibert for a place in the third round.
Results from the WTA tournament in Mallorca on Tuesday (x denotes seeding):
Maria Sharapova (RUS) bt Viktoria Kuzmova (SVK) 7-6 (10/8), 6-0
Paula Badosa (ESP) bt Alison Riske (USA) 6-7 (2/7), 7-5, 7-5
Caroline Garcia (FRA x6) bt Victoria Azarenka (BLR) 1-6, 6-4, 7-5
Shelby Rogers (USA) bt Shuai Zhang (CHN) 6-2, 6-2
Amanda Anisimova (USA x5) bt Tereza Martincova (CZE) 3-6, 7-6 (9/7), 6-4
Ons Jabeur (TUN) bt Kaja Juvan (SLO) 7-5, 7-6 (7/5)
Samantha Stosur (AUS) bt Saisai Zheng (CHN) 6-4, 7-5
Anastasija Sevastova (LAT x2) bt Varvara Lepchenko (USA) 6-3, 7-6 (7/5)
Angelique Kerber (GER x1) bt Ysaline Bonaventure (BEL) 7-5, 4-6, 6-2
Alize Cornet (FRA) bt Sara Sorribes (ESP) 6-0, 6-1