Samuel Edozie netted for the second time in a week as Saints extended their unbeaten run to 14 matches.
Winger Edozie poked in a corner before Stuart Armstrong's third goal of the season, Sekou Mara's tap-in and Carlos Alcaraz's finish punished Rovers, who had Callum Brittain sent off after two yellow cards.
Alcaraz also missed a penalty for the hosts, but they secured a fifth straight home win for the first time since 2014 and continued their best streak for 39 years.
Martin said: "We're not even halfway through the season and there is so much more room to grow.
"Hopefully we can have more days like today, but even when we have only been winning by one goal in our eyes it has been convincing.
"You can't always win convincingly, not even the teams. at the top are leaving teams in their wake.
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