The Scots – who will have home advantage for the single-leg semi-final – will discover who from Bulgaria, Hungary, Israel and Romania they will face when the draw is made on Friday.

Norway or Serbia will await the winner but Clarke is confident his side can finally end their long stint in the international wilderness.

He said: "With this group of players, I can be very optimistic about the play-offs.

"They are 100 percent committed to their country and are desperate to get to a major finals at Euro 2020. So we can be very optimistic."

There were less than 20,000 inside Hampden to see two goals from John McGinn either side of a Steven Naismith header secure victory.

But many would have been forgiven for thinking they were about to see a repeat of the Scots' catastrophic Group I opener, when the team then bossed by McLeish slumped 3-0 to the Kazakhs during a dismal defeat in Nursultan.

The hosts were booed off at half-time after defender Scott McKenna allowed Baktiyor Zainutdinov to lash the visitors ahead with a stunning 34th-minute opener but Clarke was pleased with his side's reaction.

"I thought the performance was good – good in the first half and really good in the second half against a dangerous opponent," he said.

"We knew if we made mistakes in possession, Kazakhstan could hurt us on the counter-attack which they did when they took the lead.

"But it was a great reaction from the players, in the second half particularly.

"We played a lot of good stuff, looked a threat going forward and created a lot of chances.

"It's another win – three wins in a row. I don't know about anyone else, but the boys in the dressing room are feeling good about themselves."

Clarke has yet to see Hampden anywhere near full since taking the job on back in the summer.

But he expects to see the Tartan Army turn out in numbers to roar Scotland to Euro 2020, which will see four games staged in Glasgow.

"I've no preferences for the draw," said the manager.

"You take what you get. It will be nice to have a little bit of clarity so we can actually start planning for the March games.

"We'll be at home (in the semi) and I think we've shown tonight we can be a good team here at Hampden.

"That place will be full I'm sure. We'll get a good atmosphere, get the team like that on the front foot and we can be OK.

"It will be nice (to see the stadium rocking). I've been here a few times myself as a supporter when it's been like that.

"It's a long way away though. We can enjoy tonight and the fact it's three wins in a row.

"But we know we still have a lot of work to do. We're not getting carried away thinking we've cracked it.

"I said before Cyprus I could see signs of improvement, little things in training, little things in the games that were getting better and we were improving.

"I said that until we started getting results I couldn't start shouting about it but hopefully other people can see there has been a little step forward."