Jason Puncheon slotted home after just seven minutes and it was 2-0 after Rickie Lambert's fierce drive squirmed through Hart's grasp, allowing Steven Davis to bundle home.
Edin Dzeko reduced the deficit as half-time approached but Barry then passed into his own goal unchallenged to put Saints on course for a first win since Mauricio Pochettino replaced Nigel Adkins at the helm.
Source: PA
Source: PA