Dykes came off the bench alongside Ryan Fraser in the 75th minute and twice headed home corners from his fellow substitute to add to John McGinn's opener as Scotland moved top of Nations League Group B1.
The QPR striker credited coach Austin MacPhee for the set-piece work and manager Clarke for making the tactical changes which saw Scotland turn the tables on their opponents.
With skipper Andy Robertson injured, Clarke took the opportunity to revert to a back four after Scotland were well beaten by Ukraine with their usual three-at-the-back system in June, albeit without the influential Kieran Tierney.
Scotland improved when Clarke moved an extra man into midfield during that 3-1 World Cup play-off defeat and they dominated the vast majority of the Nations League game after he started with Scott McTominay in the middle of the park.
Dykes said: "Credit to Austin, set-play manager, he has been very good since he came in.
"When I was coming on, he told me to go front post. I went front post twice and scored two, so well done to him and the whole staff.
"The manager has probably watched that Ukraine game back 100 times and went back and thought maybe he could change things himself. He has changed things this game and credit to him, it has come off. We are happy for him as well.
"We were very determined (to right the wrongs). Everyone stepped up and wanted to show the fans that we could have done better. Now we are focused on this group and we did that."
Dykes, who went off at half-time against Ukraine last time out after failing to shake off an injury, has scored six goals in his last seven internationals.
"When I hit the back of the net, it's the best feeling, especially scoring in front of all the fans here," the former Queen of the South and Livingston forward said. "It's something you won't ever forget.
"I feel really at home here, I feel like I play really well under the manager and the boys are great.
"Obviously I had a little bit of a bad spell with injuries in the last few camps which I was disappointed with, because I was on a good run.
"But I'm still on that run and I'm feeling confident every time I come here. I am just going to keep getting in those positions.
"The manager said when I was coming on 'make sure you impact the game' and I was happy to do that.
"But I was just happy to get the three points for the team because it was a big three points for the group."
Clarke, meanwhile, insists he was "expecting" Scotland to get the breakthrough as they missed chance after chance before eventually beating Ukraine at Hampden Park.
After a goalless first half in the Nations League Group B1 game, striker Che Adams and midfielder Stuart Armstrong missed good opportunities to put the Scots ahead and some frustration could be felt in the stands.
However, in the 70th minute skipper McGinn fired in a drive before substitute striker Dykes headed in twice from fellow replacement Ryan Fraser's corners.
Scotland moved two points clear of the visitors at the top of the table ahead of the visit of Republic of Ireland on Saturday, which comes before the final fixture against Ukraine in Poland next week.
On the missed chances, Clarke said: "When you are on the sidelines and you are watching and your team is creating chances, you know your team has good forward momentum, you are just waiting.
"You are actually expecting one of them to go in because you are creating so many good chance that you believe in your players and trust them to get the goal and that's what happened.
"It was a good performance and we are really pleased with it. Congratulations to the players, we give them a lot of information in a short pace of time, most of it boring.
"Walk-throughs on the pitch, meetings in the meeting room, but we took it on board, executed what we wanted to do well.
"It was a good game. We got on top of the second half and the first goal was always going to be crucial.
"Now we have to go away and reset and get ready to go again on Saturday.
"We rest and recover and get ready for a tough game against Republic of Ireland on Saturday.
"Obviously we went out there in the summer and didn't do ourselves justice (0-3 defeat) and we want to do ourselves justice on Saturday."
Clarke admitted the first-half injury to Everton right-back Nathan Patterson - which saw him taken away on a stretcher - "doesn't look like a good one", before adding: "Fingers crossed it's not too bad."
The Scotland boss was delighted with the reaction of Dykes and Fraser after admitting neither were best pleased to be starting on the bench.
He said: "It was nice for the two substitutes Ryan and Lyndon to come off the bench and make the scoreline better.
"It is credit to the players. I would say both of them probably had the hump with the head coach that they didn't start the game but that's what you want, you want a hungry group."