Second-half efforts from Jozsef Varga and Zoltán Kiss provided Debreceni VSC with a 2-0 cushion to take to Sweden for next Wednesday's return.
The Hungarian champions had to wait 73 minutes to open the scoring before Kiss added a crucial second with a spectacular second goal four minutes from time. The game had required something special to break the deadlock with neither side capable of the creativity needed in the opening half. Daniel Mendes's effort was parried by the hosts' goalkeeper Vukašin Poleksić while Gergely Rudolf's header was kept out by a flying save from Petter Wastå at the other end.
The second half was more open, however, with Leandro and Rudolf testing Wastå from distance. Kalmar responded with Rasmus Elm's drive, which forced a smart save from Poleksić, but the visitors were immediately caught on the counterattack as substitute Loránt Oláh crossed for Varga to slide in to score. Within moments, Oláh fired a presentable chance over from close range while Elm's fierce 35-metre free-kick was punched over by Poleksić. The Debrecen No1's intervention proved critical late on when Kiss rifled a low strike across Wastå into the bottom corner following a Tibor Dombi throw-in.