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And he retained his place in the starting line-up for Saturday's clash at Stamford Bridge, which ended in a convincing victory for the hosts.
Mason Mount, Pedro, Willian and Olivier Giroud all found the net as Everton were blown away in a 4-0 thrashing.
Gilmour was a rock in the Blues midfield, completing 74 passes - more than any other player on the pitch - with 92.5 per cent accuracy to keep his team constantly moving.
When quizzed on the past seven days after the game, the teenager admitted that he was on top of the world.
"It was amazing, it was a dream come true to make my full debut, but most of all getting the three points and carrying on winning," he told Sky Sports after the final whistle.
"Hopefully we continue that on the way forward."
Gilmour revealed that his start came as a surprise, finding out about his inclusion just hours before kick-off.
"[I was told] this morning, just before the game, I was eating and we got told the team," he laughed.
The Glasgow native has represented Scotland at every level from Under-15 to 21, and admits it would be "amazing" to get the nod for the senior side.
"It's a bit mad to be fair," he added. "It would be amazing to get called up.
"I need to keep working here and going my best and hopefully get that opportunity soon."
Goalscorer Giroud praised his young team-mate, stating that Gilmour is showing enviable maturity for such a young player.
"He's done very well again today. For a young player of 18 years old he's got great maturity and also listens to advice," the France international explained alongside Gilmour.
Saturday's win keeps Chelsea comfortably inside the Champions League qualification, with the Blues now enjoying a five-point lead over Wolves in the race for European qualification.