Liverpool centre-back Lovren played the full 90 minutes in Nizhny Novgorod and helped his country to a comprehensive win that seals their progress from Group D.
Lovren produced a superb, last-ditch block to divert Maximiliano Meza's shot over the crossbar early on in what was an evenly-matched first half.
But Croatia exerted their authority following the break, and Ante Coric put them ahead eight minutes after the restart.
Luka Modric's wonderful long-range effort duly doubled the Croats' advantage, before Ivan Rakitic's late strike put the gloss on a victory that ensured they reached the first knockout round with a pool fixture to spare.