Goals from Ashley Stott and Adam Morning put the Shaymen ahead at half time, but it was Gedman who took centre stage after the break to complete a comfortable win.
And the man on loan from Droylsden, who made two substitute appearances for Town in 2002, only narrowly missed out on completing his hat-trick.
"Quite a lot went right, he said. "But I would have liked to have got a hat-trick," he said.
"I had a chance when a shot from Lincoln came back off a defender but I will take two.
"The shout at half time was to make sure they did not get a sniff.
"And we were looking for the early goal to kill them off."
Gedman only trained with his temporary teammates for the first time on Thursday, but soon settled into role alongside Stott.
"It is a bit difficult getting to know the lads," he said. "But this is football.
"We have been playing for quite a while and it is universal.
"Ashley said to me that he needed a break. He is all about getting in behind defences and is the type of player I want to play with.
"He has some good qualities and sniffed out that goal before half time.
"I think we can work well together."
Gedman is now looking forward to his first match back at the Shay - after a six year gap - when Town entertain Warrington in a league game tomorrow evening.
"It was a bit brief last time," he said. "But it is a great stadium and a great pitch.
"And it is exciting to play in front of all the supporters.
"It is a challenge because the opposition sides will come to Halifax and raise their game.
"It is something that we have to deal with."
Gedman left the field at Ryton with five minutes remaining suffering from cramp.
But he is looking forward to getting a few games under his belt in his month-long stay at the Shay.
"I missed a lot of pre-season," he said. "I joined Droylsden late.
"I got through the first few games on adrenaline, but had cramp towards the end at Ryton.
"I need to get fitter and sharper so it is a crash course in the eight games this month."