Walder scored a hat-trick and converted eight of his side's 14 tries at Stadio Tommaso Fattori.
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.