Those wins mean Telford are now secure in third place in the Laidler Conference, albeit having played three fewer games than second-placed Sheffield.
Assistant Coach Jason Parry was delighted with his side’s turnaround against the Welsh outfit, following their relatively disappointing performance in Yorkshire.
He said: “We showed a lot of character in our performance against Deeside and kept it really tight all the way through.
“In the first period, they scored first, then we came back, then they went ahead again, before we equalised. It was one of those games and when we managed to get ahead in the second period, they pegged us back later on.
“Thankfully, we managed to hold on when we scored again in the third period.
“We had quite a few penalties against us, so the guys had to dig deep to get the two points.”
Saturday’s goal came courtesy of James Smith (4), Joe Aston, Macaulay Heywood, Karol Jets, Russ Plant and Joshua Hustwick.
On Sunday, meanwhile, Telford’s scorers were Macaulay Heywood, Joe Aston and James Smith (2).
Parry added: “Saturday night was a good wake-up call for us and the guys really improved.
“Deeside were very much improved from their last game against us and in their own rink it was very tough.”