With just Katowice to play tomorrow, they go into the game knowing victory will put them into the January event.
They got the best of starts when Pat Dwyer opened the scoring after eight minutes, getting the better of Thomas Tragust in the Ritten goal.
But two goals a couple of minutes later turned the game briefly in the Italians’ favour, as Simon Kostner and Alex Frei both netted.
But Blair Riley tucked away a rebound late in the opening session, from Darcy Murphy’s initial shot to level things up at 2-2.
Riley’s second and Giants’ third in the early stages of the middle stanza was the goal that proved to be the clincher.
They kept it going though to make sure as Francis Beauvillier’s angled shot opened up a two-goal lead to make things a little more comfortable.
Two more in the third period rounded things off nicely as Murphy added his name to the scoresheet five minutes in.
Then Jonathan Boxill applied the icing on the cake as the Giants look ahead to finishing the job this weekend against the Poles.
In the day’s earlier game, Medvescak Zagreb got the best possible reaction to losing their opening match to Belfast Giants, by beating Katowice 3-2 in game two.
They were two up by the end of the first as Mike Aviani and former Cardiff Devils man David Brine got the goals.
Katowice hit back through Maciej Urbanowicz and Janne Laakonen to level, but the game was decided as ex-Nottingham Panthers man Yann Sauvé got the winner, with the assist another EIHL alumni, John Armstrong, formerly of Sheffield Steelers.
Giants and Katowice face off at 7pm in their final game, with Zagreb taking on Ritten Sport in the earlier game at 3pm.