Last updated on .From the section Tennis
After reaching the Miami Open last 16 he is two wins away from regaining the men's world number one spot.
After a long time at the top of the rankings, Novak Djokovic was overtaken by Medvedev last month.
If he reaches the semi-finals, the Russian will take over again.
The US Open champion advanced to the fourth round with a 6-3 6-4 win.
The courts here are slow, so playing against a Spaniard is not easy, but I played well.
I felt like we had a lot of rallies where he was bringing the pace down and I couldn't do much.
I tried to serve well, keep consistent and make less errors.
The American world number 39 will play the Russian next.
Norrie, the British number one, will face a sixth seed from Norway in the last 16 on Tuesday.