The Tait brothers had a field day as Newcastle ran in 11 tries against Spanish side Cetransa El Salvador on Saturday.
England star Mathew broke the Cetransa defensive line almost at will, and 19-year-old Alex bagged a hat-trick with an impressive display of speed and support.
Falcons coach John Fletcher said: "Cetransa were a credit to Spanish rugby today. They played with passion in the first half, even though the quality of our side came through in the second half.
"I thought Alex Tait played well and deserved his three tries, but now we have to work towards our game against Brive on Thursday. It's not much of a turnaround."
It took the Falcons only three minutes to open the scoring - winger Ollie Phillips scoring the first of his three tries - and had secured their bonus point by halftime. The Spanish amateurs began to wilt in the afternoon sun, and Newcastle ran in seven tries in a one-sided second half.
Cetransa's moment of glory came just after halftime, when No 8 Ivan Criado powered over from a well-worked quick lineout throw.
In Romania, Warriors skipper Pat Sanderson scored a crucial try as Worcester stuttered to a 18-8 win over Bucuresti in appalling conditions.
Sanderson scored the match-winning try on 45 minutes after Bucuresti fly-half Danut Dumbrava had given Mike Ruddock's men a scare with a try on the stroke of half-time to cancel out Marcel Garvey's opener.
Warriors assistant coach Clive Griffiths said: "We're pleased with the result because of the conditions. It was freezing and the pitch was waterlogged. It was a case of getting the job done and getting out of here.
"That's now two wins out of our last two games and we hope to take that into our game with Montauban next week.
"Although they never really tested us, we had to ensure we kept going for the full 80 minutes and I thought we acquitted ourselves terrificly well in difficult circumstances and the tries were decent.
"It was a good passage of play from the backs to put Marcel in and then Pat's try was set up from a brilliant drive by the forwards."
In Italy, home side Overmach Rugby Parma crashed to to a surprise 28-23 loss to French minnows Albi in Pool 1.
Parma led 13-6 at the break, but Albi winger Patrice Serre scored a brace of second-half tries as the French went to the top of a Pool likely to be dominated by English side Bath.
Finals Edition: Listen to the best guide to the European Rugby Cup Finals weekend in Dublin, which sees Leinster Rugby take on Stade Francais Paris at the RDS on Friday night in the Amlin Challenge Cup Final and then ASM Clermont Auvergne tackle Toulon in an all-French affair at the Aviva Stadium on Saturday.