The Saints forward came off the bench in the second half and produced a low shot that squirmed under Black Cats keeper Jordan Pickford, to cancel out Jermain Defoe's penalty.
Defoe had given Sunderland the lead when he converted from 12 yards with ten minutes remaining, after Saints skipper José Fonte was judged to have fouled the striker.
But Rodriguez was able to strike shortly afterwards, ensuring Claude Puel's men have started with a pair of 1-1 draws in their opening two home matches in the Premier League.
Puel made one change to the side that lost 2-0 at Manchester United in the previous outing, with Charlie Austin replacing Shane Long in attack, while Ryan Bertrand returned to fitness to make the bench, in place of the injured Jérémy Pied.
It was Saints who started threateningly, and they went within inches of taking the lead after ten minutes.
Matt Targett’s delivery from the left was flicked into the path of Dušan Tadić 18 yards out, and he brought the ball under control before unleashing a fierce half-volley that looked destined for the far top corner, only to fizz narrowly over.
Seconds later, the hosts went close again, as Austin, making his first start of the season, hit a snapshot from 25 yards, after Tadić had rolled the ball into his path, but Pickford dived to his right to palm wide.
Saints continued to probe away against a Black Cats side content to sit deep for the most part, but they offered a reminder of their threat in the 25th minute, as Patrick van Aanholt’s angled delivery from deep found Lamine Koné at the back post, just six yards out, only for the centre-back to flash his header across goal wide.
The game had drifted into a frustrating period for Southampton, and that was summed up by Nathan Redmond being shown the first yellow card of the afternoon, shortly before the half-hour mark, for arguing with referee Lee Mason.
It took until the 38th minute for Saints to carve out another chance of note, as Cédric pounced on a loose ball 25 yards out and drilled in a low, left-footed shot, but Pickford got behind it well to hold on.
Half-time then arrived and brought no changes from either side, with the first action seeing Steven Davis booked for a foul on Sunderland debutant Javier Manquillo.
Pierre-Emile Højbjerg got a sight of goal after 59 minutes, following some neat interplay outside of the Sunderland area, but his well-struck effort was deflected high and wide by Papy Djilobodji’s outstretched foot.
Sunderland quickly went down the other end and earned an opportunity of their own, as Adnan Januzaj was judged to have been fouled by José Fonte right on the edge of the area, following a brilliant run inside from the left touchline.
Fabio Borini’s resulting low strike eluded the Southampton wall, but Fraser Forster was right behind it to gather.
Steven Pienaar was then yellow carded for a heavy challenge on Højbjerg, before Puel made his first change, swapping Tadić for Long on 67 minutes.
A bursting run from Redmond in the 69th minute created some promise for Saints, but he could only curl a right-footed shot straight at Pickford from the edge of the area.
Pickford produced a stop of far greater note seconds later, as Redmond laid the ball off to Long just outside the area. The striker drilled a low shot towards the bottom corner, but the Sunderland keeper sprang superbly to his right to get a strong hand to it.
Saints were now beginning to pile on some significant pressure, and Pickford was again called into action, palming behind Redmond’s low strike from outside the box.
Puel made his second change with 16 minutes remaining, bringing Rodriguez off the bench for Austin.
While the hosts had enjoyed a threatening spell, the breakthrough ended up arriving at the other end, via the penalty spot.
Sunderland sub Jeremain Lens got down the right and sent in a low cross towards Defoe, who went to ground as he tried to spin away from Fonte.
Mason pointed to the spot immediately, much to Fonte's frustration, and Defoe confidently dispatched the spot kick into the top corner.
Saints almost responded straight away, but Rodriguez's long range drive was plucked out of the air by Pickford, as it flew towards the top corner.
Pickford was not so assured in the 85th minute, however, when attempting to deal with Rodriguez's drive from 20 yards in the 85th minute.
The well-struck ball squirmed under the Sunderland stopper to send the home fans wild and draw Saints level.
The hosts went within inches of going in front shortly afterwards, as Matt Targett whipped a superb free-kick goalwards from 25 yards, only for it to whistle just past the upright, while Romeu had a fierce shot blocked in added time, as Saints had to settle for a point.
Southampton: Fraser Forster, Cédric, José Fonte, Virgil van Dijk, Matt Targett, Oriol Romeu, Pierre-Emile Højbjerg (James Ward-Prowse 82), Dušan Tadić (Shane Long 67), Steven Davis, Nathan Redmond, Charlie Austin (Jay Rodriguez 74).
Unused substitutes: Alex McCarthy (GK), Maya Yoshida, Ryan Bertrand, Jordy Clasie.
Booked: Nathan Redmond, Steven Davis.
Goal: Rodriguez (85).
Sunderland: Jordan Pickford, Javier Manquillo, Lamine Koné, Papy Djilobodji, Patrick van Aanholt, Jack Rodwell, Steven Pienaar (Jeremain Lens 67), Lynden Gooch (Donald Love 76), Fabio Borini (Duncan Watmore 64), Adnan Januzaj, Jermain Defoe.
Unused substitutes: Maksymilian Stryjek (GK), Wahbi Khazri, Paddy McNair, Joel Asoro.
Booked: Steven Pienaar.
Goal: Jermain Defoe (80 pen)