Mara scored twice in the space of six minutes after the break and Che Adams, who set up both the opening goals, then confirmed promotion-chasing Southampton's progress with an effort of his own.
Promotion remains Southampton's priority but after extending their unbeaten run in all competitions to 24 they will relish a crack at Jurgen Klopp's Premier League leaders.
Southampton were joined by Coventry City who beat Sheffield Wednesday 4-1 to earn a tie with non-league side Maidstone United.
Elsewhere, Leeds United needed extra time to defeat Plymouth Argyle 4-1 at a rain-soaked Home Park to advance into the fifth round, setting up a tie with either Aston Villa or Chelsea, who play their replay on Wednesday night.
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