Paul Kitson, West Ham's forgotten striker, netted the crucial first goal to keep the Hammers on the European trail.
The former Newcastle striker has found himself on the bench all season as the flamboyant Paulo Wanchope and Paolo Di Canio grabbed the headlines.
But Harry Redknapp turned to the 28-year-old in Osijek and Kitson repaid his faith with the first away goal which effectively killed off the tie.
Sub Neil Ruddock smashed home a late goal and Marc Vivien Foe got the third in stoppage time after Stanko Bubalo had equalised in the second-half - but it was Kitson's strike which knocked the fight out of the Croatian side.
Kitson has barely had a look-in since playing in the first two Intertoto Cup games back in July.
Wanchope and Di Canio struck a prolific partnership in the opening weeks of the season which left him watching from the subs' bench.
After two goalless Premiership outings, however, the Hammers boss chose to pair Kitson with Di Canio and the double-act did the trick.
Kitson released the Italian in the 26th minute and then drifted into the box to meet the right-wing cross with a firm header past Domagoj Malovan which made the aggregate score 4-0.
SIJEK: Malovan, Beljan, Zebic, Vuica, Prisc (Jukic 63), Besirevic, Vranjes (Zrilic 79), Ergovic, Babic, Mitu, Bubalo (Turkovic 86). Subs Not Used: Galinovic, Grnja. Goals: Bubalo 70.
WEST HAM: Hislop, Potts, Ferdinand (Ruddock 65), Stimac, Sinclair (Newton 46), Keller, Lampard, Lomas, Foe, Kitson, Di Canio (Wanchope 68). Subs Not Used: Forrest, Moncur, Margas, Carrick. Booked: Stimac. Goals: Kitson 27, Ruddock 83, Foe 90.
Referee: J Van Hulten (Holland).