After going ahead, 3-1, at the end of the first half, Puerto Rico conceded goals in the 67th and 86th minutes but still had a chance to win in stoppage time. Cristian Arrieta hit the crossbar with a free kick from 27 yards.
Jonathan Steele had struck the woodwork earlier in the match -- the first time in the match's opening minute.
Arrieta, Fabrice Noel and Nicholas Addlery scored for the Islanders, but Cruz Azul rallied on goals by Pablo Cevallos, his second of the game, and Alejandro Vela.
Cruz Azul leads Group B with seven points four ahead of the Columbus Crew and Saprissa, which meet Wednesday in Costa Rica (delayed on FSC at 2 a.m. ET Thursday).
In Group A, Arabe Unido of Panama defeated Metapan of El Salvador, 1-0, and leads the group with seven points, pending the result of Wednesday's Pachuca-Houston Dynamo game (live on Fox Soccer Channel, 10 p.m. ET).