Nottingham Panthers must turn around a 3-1 first-leg deficit if they are to qualify for the Champions Hockey League quarter-finals after defeat in Zurich.
The hosts dominated the first period and led thanks to Samuel Gerra.
With netminder Michael Garnett in outstanding form to deny Zurich further goals, Brett Perlini levelled with a low shot 52 seconds into period two.
But third-period goals from Roman Wick and Fredrik Pettersson won the game for the home side.
It means Panthers, who have not lost at home in the CHL this season, take only a two-goal deficit back to Nottingham for next Tuesday's second leg.
Nottingham came into the tournament as underdogs and were ranked the bottom seed out of the 32 teams but have defied the odds to reach the knockout stages.
Bench coach Rick Strachan told BBC Radio Nottingham: "We were lucky to come out with only a one-goal deficit in the first period.
"But I thought in the second period we played really well. We gave them some trouble.
"The third period we played well but it was our third game in four nights and we looked tired."
Netminder Garnett turned away 31 of the 34 shots he faced and Strachan felt he led by example.
"Garnett was fantastic and kept us in it, but they all played well. They blocked shots and threw their bodies on the line," he added.
"The defence played well and moved the puck. The forwards backchecked and forechecked hard.
"That is why we are here, not because of one guy, but because of our team performances."
The second leg will be streamed live on the BBC Sport website, BBC Sport app and Connected TVs on Tuesday, 7 November.