Goals from Willian and Ross Barkley inflicted Liverpool’s third defeat in their last four games.
Gilmour was surprisingly given a starting berth by Frank Lampard, and the youngster vindicated his manager’s decision by putting in a man-of-the-match display against Jurgen Klopp’s men.
The 18-year-old pulled the strings in midfield and inspired Chelsea to beat Liverpool for the first time since 2018.
In an interview with TalkSPORTS, Cascarino said the Scottish man’s performance has reminded him of Keane, a player who was considered as one of the best midfielders of his time.
“He was thrown in the deep end and absolutely swam, he didn’t have an issue at all,” the ex-Chelsea striker said.
“In the first 15 minutes, he just set the standard for the game, just getting on it, having that inner belief and dictating the pace of the midfield.”
“Without wanting to go over the top, because I’m as guilty as everybody of doing this and getting excited about what you see, but I remember Keane being very similar at this age”
“Roy Keane demanded the ball, he was a fearless footballer.”
“When I first saw him at Nottingham Forest and then when he got in the Ireland squad, Roy just enjoyed having the ball, he demanded it, ‘give me it’.
“Billy Gilmour did that. Roy was tenacious and Billy Gilmour showed that as well last night.”
Gilmour joined Chelsea’s fabled academy from Rangers in July 2017 following his 16th birthday.