Rovers were on the back foot from the start and were undone by a lovely Saints move midway through the first half.
Kuryu Matsuki played a clever pass in behind Rovers wing-back Ryan Alebiosu to Archer, who sent a low ball in from the left for Larin to finish from close range – the Canada forward’s fifth league goal since arriving on loan from RCD Mallorca in February.
The hosts doubled their lead with a fortuitous goal a couple of minutes before half-time, punishing an error by Kristi Montgomery after he had lost possession.
Shea Charles darted in from the left and played the ball into the six-yard box – and it ended up in the net after Sean McLoughlin’s attempted clearance bounced off Manning and then Rovers’ Yuri Ribeiro.
Blackburn were much more competitive in the second half and went close to pulling a goal back when Ryoya Morishita fired the loose ball against the crossbar after Yuki Ohashi’s shot had been parried by keeper Daniel Peretz.
At the other end, Matsuki missed a sitter when he blasted over after being unselfishly teed up by Larin.
But the excellent Archer made no mistake when similarly set up by Leo Scienza, calmly steering the ball into the far corner of the net.
Southampton, relegated last season and 21st when Will Still was sacked as manager in November, are now unbeaten in 18 league and cup matches.
It has been a remarkable turnaround in a season that will include at least one trip to Wembley and could end in a return to the Premier League.