Arsenal took the lead after 22 minutes at Emirates Stadium on Saturday thanks to a shocking error of judgement by Saints keeper Boruc, who tried to dribble past Oliver Giroud in his own area only to be robbed by the Gunners striker who scored from close range.
Arsene Wenger's side deserved to be ahead at the break having also struck the woodwork twice.
The visitors, so miserly in defence this season, repelled further Arsenal attacks until the 86th minute when Jose Fonte conceded a penalty for holding onto Per Mertesacker's shirt. Giroud grabbed his second goal of the game and seventh in the league this season from the spot.
The Gunners now have a four-point lead over Liverpool at the top of the table after 12 games, while Saints remained in third ahead of Chelsea's clash at West Ham later on Saturday.
Kick-off was delayed by 15 minutes following problems on the Piccadilly underground line.
Arsenal fashioned the first opening after 11 minutes. Jack Wilshere, showing no signs of any England-related lethargy, charged into the right side of the penalty area and looped the ball over Boruc. However, it dropped onto the inside of the far post before bouncing back into the arms of the grateful Saints keeper.
The Gunners continued their patient build-up and unlocked Southampton's defence again on 17 minutes, only to be denied by the same woodwork. Mesut Ozil's cross was flicked goalwards by Aaron Ramsey, but, with the keeper beaten, the ball shaved the outside of the right post.
There was, though, no saving the Saints stopper when he gifted Arsenal the lead on 22 minutes.
Boruc - beaten by a long punt from Stoke goalkeeper Asmir Begovic earlier this month - made a complete hash of his attempted dragbacks when dwelling on the ball under pressure from Giroud. The France striker promptly robbed the Pole, and slotted home his sixth Premier League goal into an empty net.
To their credit, Southampton looked for a response - with referee Mark Clattenburg aggravating the home support with some of his decisions.
Arsenal goalkeeper Wojciech Szczesny remained alert to tip over a dipping 18-yard effort from Saints captain Adam Lallana, fresh from his full England debut over the international break.
On 40 minutes, the Poland international then produced a fine one-handed save to deny a well-executed half-volley from Jay Rodriguez, after the new England cap collected the ball on his chest before drilling it goalwards from 15 yards.
The visitors were lively again after the break, with Lallana driving a 20-yard effort goalwards following another swift counter-attack.
Arsenal continued to press for a second goal, but found little space behind the well-drilled Southampton defence.
With 20 minutes left, Theo Walcott, out since mid-September with an abdominal problem, came on for Santi Cazorla.
Arsenal were then forced into another change when Mikel Arteta hobbled off with what looked like an ankle problem, and Czech playmaker Tomas Rosicky came on.
Southampton refused to give up and there were some nervy moments for the home crowd during the closing stages.
Walcott, returning against his former club, flashed an angled drive across goal.
Arsenal were awarded a penalty on 86 minutes when Germany defender Mertesacker, who missed the defeat at Manchester United before the international break with a virus, had his shirt pulled by Fonte.
Giroud made no mistake from the spot, as Arsenal provided the required response to keep themselves clear of the chasing pack.