Roglic, bidding for a fourth successive overall victory, began the day 1:34 behind Evenepoel in second place and launched a stunning attack near the end of the 189km ride.
The Slovenian poured on the power on the uphill finish in Tomares to split the race with only four other riders managing to stay with him.
As the finish line loomed, Roglic was overtaken and seconds later went down heavily after clipping wheels with 100m to go.
Denmark's Pedersen (Trek-Segafredo) took the win from Pascal Ackermann (28, UAE Team Emirates) and Danny van Poppel (29, Bora-Hansgrohe) with a bloodied Roglic getting gingerly back to his bike and limping over the line in the pursuing bunch.
Evenepoel himself appeared to have suffered a late puncture inside the final 3km and required a bike change.
Initial timings suggested Roglic, despite his misfortune, had taken the red jersey with Evenepoel slipping down to third but that was soon revised with Evenepoel still on top.
He now leads by 1:26 from Roglic with Enric Mas 2:01 down in third place.
The flat stage, following Monday's rest day, had been led by escapees Ander Okamika (Burgos-BH) and Luis Angel Mate (Euskaltel-Euskadi).
But they were eventually reeled in as the pace quickened before the fireworks really began.
"I heard that Primoz crashed, so I really hope he's okay and that he can continue the race," Evenepoel said.
"We all know that Primoz is explosive so a final like this is really made for him. That makes it even more of a pity for him that he crashed. You never want somebody to crash - I hope he's okay.
“I'm happy that the 3km rule exists otherwise I would have lost a lot of time today."