Jonny Wilkinson kicked 16 points as Newcastle defeated Border Reivers 26-11 away from home.
Wilkinson played a starring role for Newcastle once more
Toby Flood ran in a first-half try for the Falcons before Matt Thompson also scored after the break, while Paul Thomson got a Borders' consolation try.
Elsewhere in the competition, Bristol pulled off an impressive 36-28 victory over Premiership rivals Northampton.
David Lemi produced a stunning display for Bristol with two tries and ended with a 20-point tally.
London Irish were also winners on Sunday, coasting to a 64-0 win over Overmach Parma at the Madejski Stadium.
Scott Staniforth ran in a hat-trick and Delon Armitage scored a brace as the Exiles ended the match with 10 tries.
On Saturday, Gloucester thrashed Romanian minnows Bucuresti 106-3 in a totally one-sided Challenge Cup encounter on Saturday.
The Cherry and Whites notched up 15 tries, with James Simpson-Daniel touching down for four of them.
West Country neighbours Worcester also earned a second successive win but were made to work far harder in Italy.
Prop Chris Horsman, centre Mark Tucker and flanker Tevita Taumoepeau scored their three tries in a 19-14 victory against Amatori Catania.
Worcester will now face a winner-takes-all match against Connacht on 10 December.
The Irish province are also just one win away from a quarter-final place after a tense 19-16 pool win over Montpellier in France on Friday.
Fly-half Paul Warwick kicked the Irish side to victory with three penalties, a drop goal and a conversion.
Winger Ted Robinson scored early in the second half and Connacht had to defend well to claim the triumph.
Meanwhile, the match between Narbonne and Viadana was abandoned after 41 minutes due to fog with the French side leading 20-14.