Neither side had conceded a goal from open play heading into this match, but a frenetic start to proceedings saw both teams net inside the opening four minutes for just the second time in a World Cup fixture.
Brought into the side for exactly that reason, Knudsen's delivery proved difficult to deal with and Jorgensen was there to tuck the ball through the body of Danijel Subasic from six yards out.
Croatia were level a few minutes later, though, as an attempted clearance in the box struck makeshift midfielder Andreas Christensen clean in the face, gifting Mario Mandzukic the chance to scuff the ball into the back of the net.
Following that thrilling start it was Croatia who were quicker to find their rhythm, coming close to a second through a Rakitic shot that Schmeichel had to slap away.
Dejan Lovren also glanced a header wide from a good position after getting between two opposition men, while Rakitic's next shot from distance was hit too close to Schmeichel.
The arrival of Lasse Schone for Christensen at the start of the second half was Age Hareide's way of acknowledging that fresh impetus was needed in midfield, with the Vatreni being allowed to dominate possession.
That alteration worked well as Denmark, in complete contrast to the first half, were on top pretty much throughout the second period.
Both teams started living up to their reputations of being tough to break down, however, with the first meaningful shot after the restart coming 73 minutes in.
Substitute striker Jorgensen swivelled after being picked out inside the box, but his shot lacked power and Subasic comfortably gathered,
Eriksen, who clipped the top of the crossbar with an intended cross in the first half, then shot wide from a good position on the edge of the area, as did rival playmaker Modric at the other end.
Perisic had a shot saved and glanced a right-sided cross over the bar as both teams looked for a late winner, but despite a combined 19 attempts there was to be no way through and extra time was required for the second time today.
Denmark's previous four World Cup knockout ties had produced 19 goals at an average of nearly five a game, but neither team truly looked like netting from open play - Pione Sisto's curler 108 minutes into the match the closest either side came prior to the penalty.
Opening goalscorer Jorgensen brought down Rebic once he had been played through on goal by Modric, but Schmeichel guessed the right way and kept out Modric's tired penalty.
Further drama was to follow in the shootout, as Eriksen and Milan Badelj missed the first two attempts.
The next four spot kicks were converted, but Schone and Josip Privaric both missed, as did Jorgensen, allowing Rakitic to win it at the end of a gruelling contest.
CROATIA (4-2-3-1): Subasic; Vrsaljko, Vida, Lovren, Strinic (Pivaric 81'); Brozovic (Kovacic 71'), Rakitic; Rebic, Modric, Perisic (Kramaric 97'); Mandzukic (Badelj 108')
DENMARK (4-3-3): Schmeichel; Dalsgaard, Kjaer, Jorgensen, Knudsen; Eriksen, Christensen (Schone 46'), Delaney (Krohn-Delhi 98'); Braithwaite (Sisto 106'), Cornelius (Jorgensen 66'), Poulsen