Tongan winger Holo Taufahema was Caerphilly's hero with a hat-trick of tries as the Welsh side made as stirring comeback against their Italian opposition.
The Castletown men trailed 25-8 as halftime neared and they looked down and out- but their never-say-die attitude as they fought back had their fans in raptures.
Parma ran in three early tries through backs Corrado Pilat, Norman di Maura and Leone Larini- but two of them were gifted as Caerphilly's defence blundered badly.
But Taufahema rallied Caerphilly with his powerful running and finishing strength and was ably supported by replacement flanker Gareth Jones.
Jones grabbed a brace of second half tries as Caerphilly upped the tempo and forced Rugby Parma
on the defensive.
They went on a 28-point try spree in the second half with just a penalty in reply from their battered opponents.
Lock Paul Jones scored Caerphilly's sixth try with Justin Thomas landing one conversion and three penalties.
But Caerphilly's performance was marred by the sending off of full back Seone Tuipolutu who received two yellow cards for high tackles and is likely to miss the second leg next weekend.