The home side rushed out of the blocks and Mathieu Debuchy saw his fourth-minute volley fly wide of the post.
Only a goal-line clearance from Calum Chambers prevented Loic Remy from giving the Magpies an 11th-minute lead after Gouffran had nicked the ball from the grasp of Paulo Gazzaniga to set up his compatriot.
Newcastle took the lead in the 27th minute when Jos Hooiveld swiped at thin air when attempting a clearance, which left Gouffran with the task of rounding a stranded Gazzaniga and tapping the ball into an empty net.
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The home side continued to push the visitors inside their own half, and Vurnon Anita beat two defenders before flashing a good ball across the face of goal, but no Newcastle attackers were on hand to tap it home.
However, it was the home side who had the game's next chance, as Remy fired a low shot towards goal which was tipped away by Gazzaniga.
Southampton slowly grew into the game, though, and Steve Davis rattled the bar in the 63rd minute, but the score was level 60 seconds later.
Rodriguez broke with the ball and played a one-two with Davis before slotting the ball beyond Tim Krul to round off an incisive counter-attack.
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Both sides pushed for a winner in the final 30 minutes and good chances fell to both teams.
Debuchy fired straight at Gazzaniga in the 68th minute, while Rodriguez saw his weak header saved by Krul at the other end.
Remy pounced on a scuffed Gazzaniga clearance in the 73rd minute, but the unmarked Frenchman inexplicably fired well wide of goal from just six yards.
In the final minute of normal time, Debuchy raced back to nick the ball off the toes of Rodriguez, who seemed certain to give his side a late winner, but both teams had to settle for a point.