Eight minutes (and two yellow cards) later Croatia responded with a 39-minute goal from Andrej Kramarić.
Lovren will now come up against Liverpool teammates Jordan Henderson and Trent Alexander-Arnold in Wednesday night's World Cup semi-final.
Defender Mario Fernandes was momentarily a national hero after dragging the game back from the brink and heading home deep into extra-time, in doing so cancelling out a Croatia strike and forcing a penalty shootout.
Croatia won against host Russian Federation 4-3 on penalties after the two teams maintained a 2-2 tie by the end of the extra time in the World Cup quarter-final.
The Croats hadn't advanced to the semifinals at the World Cup since 1998, when the country made its first appearance.
Croatia goalkeeper Danijel Subasic, already hobbled with a leg injury, could do nothing but watch it hit the net.
"22 "Fiery Ones", One Heart, One Soul, One Croatia!" trumpeted the Sportske Novosti paper, featuring photos of the players.
Rakitic then scored his second penalty shoot-out victor in two games.
Then in 1990 in Italy they beat Cameroon in extra time to head into another semi-final, this time they faced Germany and lost on penalties, the beginning of their long hoodoo from 12 yards.
"This is a handsome feeling, we are overwhelmed, This win was for the whole of Croatia and Croats around the world".
Russian Federation shocked Spain in the last round after drawing 1-1 and then beating them on penalties 4-3.
"It wasn't a handsome game, but it was a battle", Dalic said.
Modric and Rakitic were decisive in the shootout but didn't play up to expectations in regulation and extra time, unable to create many significant chances for Ivan Perisic and Mario Mandzukic up front.
Saudi Arabia and Egypt were swept aside in the group stage.
Cheryshev was Russia's leading scorer at the World Cup with four goals. In the first halftime, we should have had more control of the ball, while in the second half we were dominant.