Goals from Ryan Christie, Lewis Ferguson and Lyndon Dykes turned the game around for the hosts after Kostas Tsimikas had given Greece a deserved lead just past the hour mark.

The Tartan Army had nothing to celebrate in the first half at Hampden Park when Scotland failed to muster a shot on target, with the visitors dominating possession but squandering opportunities.

Tsimikas made the breakthrough in the 62nd but Scotland hit back with Christie's surprise equaliser two minutes later after a video assistant referee (VAR) review.

Ferguson then grabbed a scruffy but sweet first international goal in the 80th and Dykes made it 3-1 three minutes into stoppage-time after a goalkeeping howler by Konstantinos Tzolakis.

Vangelos Pavlidis could have scored for Greece in the eighth minute but, unmarked at the back post, failed to get a final touch to a pass across goal from captain Anastasios Bakasetas. Georgios Masouras also fired over in the 54th.

Clarke said his side deserved it in the end.

"On the performance side of it, you have to understand how hard we worked out of possession," he said.

"When they scored the goal, the shackles came off a bit, and from there we finished the game strong.

"The Greeks had a lot of the ball in the first half, but they weren't carving us open.

"Football is a 90-minute game, and you have to make sure you come out of it with a positive result. 3-1 maybe flatters us, but we did enough to win the game.

"It gives us three points and takes us one step closer to what we want to do.

"Lewis Ferguson and Ryan Christie both miss out. Aaron Hickey has picked up a small injury, so I've got a bit of thinking to do.

"We can only concentrate on ourselves. We have to win here and see what the situation is after that."

The match was Clarke's 71st at the helm and he will beat Craig Brown's record when his still-unbeaten side hosts pointless Belarus on Monday (AEDT) in a game that could secure at least a play-off spot for next year's finals.

Scotland is level on seven points with group leaders Denmark after three games, but behind on goal difference.

Greece, the 2004 European champion, has three points and is teetering on the brink of an early exit with a crucial game away to Denmark on Monday (AEDT).