Rafael Nadal reached the third round at the Madrid Open with an impressive straight-set win over Australian Alex de Minaur.

The Spaniard, 37, won 7-6 (8-6) 6-3 to take revenge on the opponent who knocked him out of the Barcelona Open 10 days previously.

Five-time champion Nadal is playing on the Madrid clay for the final time, in what he expects to be the last season of his career.

He will face Pedro Cachin next after the Argentine beat American 20th seed Frances Tiafoe 7-6 (7-1) 3-6 6-4.

"I am super-happy to be competitive against a player like Alex de Minaur," Nadal told Sky Sports.

"Tennis hasn't been the issue, it is more the physical issues. If I am able to play tennis, I will see how far I can go. Step by step, let's see how I recover."

British number one Cameron Norrie recorded a comfortable 6-1 6-4 win over Brazil's Joao Fonseca to set up a meeting with Norwegian fifth seed Casper Ruud, who beat Miomir Kecmanovic 6-4 6-1.

Italian world number two Jannik Sinner and Russian third seed Daniil Medvedev both also progressed.

Australian Open champion Sinner, 22, beat compatriot Lorenzo Sonego 6-0 6-3, while Medvedev came from behind to win 2-6 6-4 6-4 against Italy's Matteo Arnaldi.

However, Greek sixth seed Stefanos Tsitsipas - champion in Monte Carlo earlier in April - went out following a 6-4 6-4 loss to Brazil's Thiago Monteiro.

Nadal said this week he will only play at the French Open next month if he feels "capable enough to compete". This performance will give him the belief that he can.

Seeking proof of his readiness before the Grand Slam at Roland Garros, which starts on 26 May, he delighted the home crowd with a display that certainly suggests he can further extend his Madrid farewell.

Nadal had made the perfect start by claiming an early break of serve, but he had to fight back to force a tie-break after De Minaur won four of the following five games.

The 22-time Grand Slam winner took control of the tie-break, establishing a commanding 6-2 lead, but squandered four set points before prevailing.

Crucially, Nadal maintained that momentum and asserted himself with an immediate break in the second set.

Chants of "Ole, ole, ole, ole" rang around the Manolo Santana stadium court as Nadal reached his first match points, and the record 14-time French Open champion repeatedly punched the air in celebration after sealing a significant victory.

Nadal was making his return from a three-month injury absence at the Barcelona Open and, having barely played last year, will hope this promising victory can provide a springboard for the remainder of the season.

However, he later reiterated his stance that he would not appear at Roland Garros next month unless he senses a run deep into the tournament is possible.

"For me, Roland Garros is the most important tournament of my tennis career," Nadal said.

"It's not about losing or winning. If I am not able to go on court and dream - even if it's the minimum, minimum percentage - for me it doesn't make sense to go on court.

"I prefer to stay with all the amazing memories that I have. And it's best of five [sets], so it's a different story. If I know before the tournament that my body will not hold for the whole tournament, I will not be on court."