Mathias Jorgensen put the Danes ahead inside the first minute in Sunday's last-16 tie in Nizhny Novgorod, but Mario Mandzukic quickly brought Croatia level.
Liverpool defender Lovren glanced Luka Modric's free-kick wide late in the first period, before the sides played out a keenly-contested - and goalless - second half.
Neither could force a winner during extra-time either, with Kasper Schmeichel saving a 116th-minute penalty from Modric, meaning spot-kicks were required.
And it was Lovren's team that prevailed 3-2 in the shootout to book a quarter-final clash with hosts Russia on Saturday.