Gilmour has now become the youngest ever scorer in Scotland U21 history, although his goal was overshadowed by a magnificent solo strike from West Bromwich Albion winger Burke.
Manager Scot Gemmill was thrilled at the performance and is eagerly anticipating a rematch with England in Aubagne on Wednesday after losing at the same stage to the same opponents last year.
“It’s very exciting to look forward to the occasion,” he said. “Every time the teams meet there’s a real sense of occasion.
“It’s going to be the same again. The key thing is this year we have an extra day’s rest. Last year I can remember feeling that was a factor. We are going to need every ounce of energy to really find a way to win. That extra day could be the difference. We’re really proud of the players. It’s great justification to [SFA performance director] Malky Mackay for finding the budget to get us here because it costs a lot of money. It’s not a free invitation. There is a big responsibility to come and do well.
“We have got a lot of players who are eligible but weren’t available because of injuries. We take real confidence that we’re starting to put together a real squad of players.
“We have a bigger selection and real depth. A lot of people in Scotland are questioning where the young players are. Performances like this are very good to help convince people good work is happening, not just with us but more importantly the clubs as well.
“I hope the goals are a snapshot of how good Billy and Oli can be. Billy showed his level today. It’s not just his technical ability, it’s game intelligence and composure.
“As for Oli, a lot of people are still waiting to see him really fulfil his potential. He came here last year and scored an impressive goal. And it was the same today. It’s difficult not to say ‘wow’ when he does that.”
The Scots enjoyed a dream start, taking the lead after just 84 seconds. Rangers’ Glenn Middleton accepted Greg Taylor’s pass down the left flank and created space before pinging the ball across goal to Gilmour. The former Ibrox youth had traffic in front of him, but that wasn’t a problem as he deftly dipped a shoulder to create a path to goal and curled a superb effort into the corner of the net.
Gilmour was thrilled. “That goal is up there with any I’ve ever scored, especially as it was my first goal for the Under-21s in just my second start,” he said after the game.
“The manager has given me a lot of confidence this week and today I was playing a slightly different position because I was higher up alongside the strikers.
“To get seven points out of nine and to go through on top is brilliant. We got off to a great start with the two goals, but we really had to dig in at the end because they were playing 3-1-6 to try and get the equaliser.
“We’re still unbeaten. The first game wasn’t great against Togo [it finished 1-1], but credit to the boys because we have reacted brilliantly after that.”
It got even better for the Scots when they doubled their advantage in the eighth minute with a simply incredible goal from Burke. He collected the ball inside his own half and, after combining with Fraser Hornby, he showed just why his combined transfer fees have reached £28 million.
He powered his way through, shrugging off challenge after challenge, before racing to get to the ball before the onrushing keeper and clipped a delightful finish into the net.
Scotland were increasingly pinned back as the second half progressed with their ball players unable to make the same impression as in the opening 40 minutes.
And it was panic stations with eight minutes to go when the Koreans deservedly clawed themselves back into the game when Kangin Lee curled a free kick into the net from 25 yards out with Doohan unable to keep it out despite getting a hand to it.
Scotland held on and their Toulon adventure will now continue.