Adam Armstrong bagged his fourth goal of the season after Samuel Edozie and Jack Colback had cancelled each other out in the first half.
Saints were without Che Adams who is wanted by Everton and Bayer Leverkusen-bound Nathan Tella after weeks of uncertainty around the likes of James Ward Prowse and Romeo Lavia.
"There has been so much change and disruption so I am pleased with the mentality of the group," Martin said.
"Che wasn't in a place to give it everything he's got. He and Nathan both played last week despite the noise but it has been a long week for both of them.
"The first half was no where near good enough but the subs were important and we persevered.
"I'm pleased we won, but I'm not happy with the amount of moments QPR had and how we reacted to scoring again.
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