Liverpool's No.6 played the full 90 minutes and gave an assured display at the heart of the defence, including one fantastic challenge in his own penalty area to block a dangerous effort.
Croatia took the lead on 32 minutes when a header from Mario Mandzukic that appeared to be going wide was deflected into his own net by the unfortunate Nigeria player Oghenekaro Etebo.
The second goal arrived from the penalty spot on 72 minutes. Mandzukic was hauled back by William Troost-Ekong and Luka Modric made no mistake from the resulting spot-kick.
Lovren and Croatia are back in action on Thursday, when they take on Argentina.