Prop Robbie Morris, flanker Cory Harris and England centre Jamie Noon scored two each as the hapless Italian defence leaked 40-plus points in each half.
The Falcons ran in seven tries on their way to a match-winning 41-0 lead at half-time, and repeated the dose in the second spell.
At Sixways Stadium, Shane Drahm's 20 points inspired the Warriors to a valuable 30-20 victory over Connacht.
The victory gave Worcester the lead in Pool 5, but they face a tricky trip to Connacht next weekend before they start thinking about the quarter-finals.
Warriors director of rugby John Brain admitted: "We had to work hard out there - no-one ever beats Connacht heavily.
"We went in for a try at the end and denied them the bonus point but we need to improve our performance to get a result."
The Warriors struck the opening blow with a try to full-back Nicolas Le Roux, but the 17th-minute sin-binning of skipper Pat Sanderson proved costly.
Connacht fly-half David Sleman converted the penalty and then added the extras to centre Keith Matthews' try.
Drahm converted his own try to give the home side a 14-10 lead at the break and the Warriors needed the Australian's reliable boot to keep their noses in front.
Three second-half penalty goals from Drahm cancelled a Matt Mostyn try but the match went right to the wire.
The Warriors led 23-20 for the final quarter until a last-minute try to back-rower Drew Hickey sealed the victory.
Northampton fullback Bruce Reihana was among the try-scorers in the Saints' 32-20 home win over Narbonne and the Kiwi's 12 points with the boot proved the difference on the day.
Reihana and backrowers Dan Browne and Sam Harding gave Saints a handy 20-7 lead at half-time but Narbonne's gritty comeback will sound the alarm bells ahead of the English club's trip to France next weekend.
The win moves the Saints to the top of Pool 1 alongside Bristol but Narbonne are poised behind and cannot be discounted with two matches at Parc des Sports et de l'Amitie still to play.
In a Pool 3 match, Bayonne ensured Bucuresti remained at the bottom of the table with a 38-10 win in Romania.
Former Scotland centre James McLaren scored the first of the French club's six tries.