Hard courts have always been the surface that best reward Madison Keys’ fast, flat shots.

As the year dawned, she won her first 12 matches on those quick courts in Australia, taking the title in Adelaide, then winning her first Grand Slam singles crown in Melbourne.

Coming into the Cincinnati Open, the 30-year-old American’s hard-court record was a lofty 20-3.

And while Keys seemed in doubt for virtually all of the match, she rallied to score a draining 1-6, 6-3, 7-6 (1) win over up-and-coming Eva Lys.

Keys saved two break points to get to that deciding tiebreak, then threw the hammer down, winning seven of eight points. When it was over, Keys raised both her arms and pumped her fists — more in relief than jubilation at her favorite tournament on tour.

“I just kept trying to listen to everyone here cheering me,” Keys said in her on-court interview. “It helped me get back into the match and across the finish line.”

In many respects, the comeback victory was typical of Keys’ breakthrough season. She’s now won 10 matches after losing the first set and 15 that went the distance — both the standard on the Hologic WTA Tour.

Keys has won 18 matches in Cincinnati, her highest single-tournament total after Charleston (21).

On Monday, Keys will play a third-round match against qualifier Aoi Ito, a 24-year-old from Japan ranked No. 94. Ito defeated No. 27 seed Anastasia Pavlyuchenkova 6-1, 4-6, 6-4.

After winning the Australian Open, Keys has occasionally struggled against lower-ranked players. While her record for the season against players outside the Top 50 this year is 14-4, three of those losses have come since June.

Meanwhile, in seven encounters with Top 10 players, Lys had never taken so much as a single set, most recently in a 6-2, 6-2 third-round defeat by Iga Swiatek.

But playing her first match against Keys, Lys looked like a different player. She broke Keys in her second service game when — in a pattern that repeated itself numerous times — Keys sent a short backhand into the net.

Lys broke her again to take a 5-1 lead and, serving for the set, weathered two break points. At deuce, Keys slapped two returns long — her 19th and 20th unforced errors of the set.

With Lys serving at 1-0 in the second set, it started to come together for Keys. The hard, flat forehand started to find the court and at the 38-minute mark Keys had her first break of service.

But Lys got it right back when another Keys forehand landed in the net. Keys returned the favor to take a 3-1 lead, breaking Lys at love. That margin held for the remainder of the set after Keys converted her fourth set point. Lys finished that frame with only three winners — and 17 unforced errors.

Keys seemed to be in a precarious position, trailing 3-0 when the forehand started to fire. She hit a gorgeous running forehand winner down the line to win her first game, and the momentum continued. Keys broke Lys at love to get it back on serve. On the way to 3-all, she won 10 straight points.

Serving at 3-4, Keys double faulted to give Lys a tantalizing break point, which would have had her serving for the match. Keys responded with an ace — her third of the game — and leveled it when Lys missed a forehand.

For the entire match, Lys had matched Keys with great anticipation and some aggressive play. But serving at 4-all, for the first time, her nerves betrayed her. At 30-all, she hit an anxious forehand long and then double-faulted to put the match on Keys’ racquet.

Naturally, Lys broke back for 5-all, converting her third opportunity, stopping a blistering forehand from Keys with a deft forehand volley winner. After Keys saved those two match points, the match entered the final tiebreak, which Keys won decisively when Lys’ forehand broke down.

Keys weathered 71 unforced errors (against only 29 winners) but managed 12 aces, most of them in crucial situations. She held a 99-96 edge in points and Lys actually finished with one more service break, 5-4.

Bouzas Maneiro rolls again

Jessica Bouzas Maneiro continued her hot play, defeating No. 21 seed Leylah Fernandez 6-3, 6-3. The 22-year-old from Spain reached the quarterfinals a week ago in Montreal and has now won six of her past seven matches.

Bouzas Maneiro — who won 23 of her 28 first-serve points — played a solid first-round match against wild card and seven-time Grand Slam champion Venus Williams.

Fernandez made a splash, winning the title in Washington, D.C., but lost her first match in Montreal to Maya Joint.

A singular achievement for Townsend

Taylor Townsend is No. 1 in the PIF WTA Rankings, but she also continues to make impressive showings in singles.

Granted a wild card into the main draw in Cincinnati, she was a definitive 6-2, 6-4 winner over No. 13 seed Liudmila Samsonova. That came after she reached the quarterfinals at the Mubadala Citi DC Open after losing to Leylah Fernandez.

Rybakina comes back

In their first meeting, No. 9-seeded Elena Rybakina rallied to defeat Renata Zarazua 4-6, 6-0, 7-5.

Rybakina, who stroked 14 aces, won 40 of her 50 first-serve points and saved seven of the eight break points against her. She now has a 20-4 record against opponents ranked outside the Top 50 this year. This is her sixth appearance in Cincinnati, the best showing came three years ago when she reached the quarterfinals.

Rybakina will play the winner of the later match between No. 19 Elise Merten and 19-year-old qualifier Clervie Ngounoue on Monday.