Costa staged a late attack as part of a group on the final climb to the finish, catching Kron who had been part of an early breakaway.
As the two riders passed Hermann Pernsteiner (Bahrain Victorious) with 150m to go, Costa swung from the right side of the road to the left in a wild maneuver which caused Kron to take evasive action.
Kron was visibly angry with Costa after crossing the finish line, as it was confirmed shortly after the sprint was being investigated by UCI commissaires.
The investigation deemed Costa to have been in breach of the rules and so he was relegated to second place, with Kron awarded the victory.
The Dane was happy with the outcome of the review, seeing no controversy with the commissaire's view of the incident.
"I'd need to see the sprint myself," Kron said. "But we can say the jury have taken the decision and I trust the jury, and I'm the winner and I'm happy for it.
"Yesterday I was disappointed to miss out in the GC after my team had worked so good for me in the last day. It's nice to give something back to all the riders. It's for the team."
Richard Carapaz (INEOS Grenadiers) maintained his overall lead on the race with two stages left, crossing the finish line 2 minutes and 49 seconds behind Kron and Costa, with 26 seconds on Jakob Fuglsang (Astana) in second.