Peter Horne was the Warriors' hero - coming off the bench to score the decisive try to chalk up the Scottish side's first RaboDirect Pro12 win of the season, while Leinster have now lost two of their first three.
Five years ago, Glasgow were blessed with a glut of promising talent including Johnnie Beattie, John Barclay and Moray Low - all of whom have gone on to represent Scotland.
And Lineen believes history is set to repeat itself.
"There were eight guys below the age of 22 starting [against Leinster], it is an incredibly young team," said Lineen.
"We've trained really well and brought in good players. We've now maybe not got the flashy players but we have the quality of team spirit and the guys work really hard for each other.
"There is a new group of players coming through, which also happened four or five years ago.
"When we get the guys believing, giving them confidence, a game plan, getting the selections right, then all the guys buy into it.
"They have worked incredibly hard for the past few months and I am so pleased for them."
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