Nevin started well and got through with a series of decent right hands to take a 5-3 lead after the first round.
The Irishman outboxed Alvarez, who was struggling to land a glove while also being on the receiving end of Nevin's shots.
Alvarez began to show signs of warming to the contest at the end of the second, but still found himself trailing by three points heading into the final round.
Nevin came under some pressure early on, but weathered the storm and came out fighting. He landed a few quick right hands, which seemed to make his lead unassailable.
The judges rewarded Nevin for a terrific performance by scoring the bout 19-14 in his favour.