Perisic was taken off in that game but returned to the starting line-up on Sunday as his country won 3-1 to claim top spot of Group A1.
Ex-Spurs star Luka Modric put Croatia in front before a quick equaliser from the hosts. Perisic was the man to cross for Marko Livaja’s headed winner on 69 minutes before Dejan Lovren sealed the points.
Boss Zlatko Dalic said: “It was a really big result and a win in a tough game. We took the lead and conceded a goal. It was a great fight, so I congratulate the boys even more, they invested maximum effort and energy.”
Elsewhere, Hojbjerg completed the match as Denmark beat France in Copenhagen to finish second in their Nations League group.
Ben Davies was absent through injury as Wales lost to Poland.