After watching from the bench in midweek as his club mates featured for England, Rodriguez seized the initiative just before half-time.
With Palace committing men forward to attack, the England forward took a fine touch on the halfway line to leave two defenders in his wake before an on-rushing Julian Speroni failed to intercept outside his box, leaving Rodriguez to poke home as he sat on the floor.
Tony Pulis' side returned from the break with added impetus and could argue Dejan Lovren deserved to be shown a red card when he chopped down Yannick Bolasie on the edge of the box. The Croatian only received a yellow card from Howard Webb, before Mile Jedinak wasted the subsequent free-kick.
Try as they did, Palace were unable to forge a significant opening and Artur Boruc was seldom challenged as Saints held out to return to winning ways.
The match began slowly with Rodriguez and a weak Glenn Murray penalty appeal the only moments of note until the ninth minute, when Speroni produced a wonderful save to deny Steven Davis - unaware the offside flag had been raised.
It was one of few clear-cut chances created by Southampton in a frustrating opening 30 minutes, with diligent Palace defending meaning their possession counted for nothing.
Murray and Rodriguez had efforts blocked in that period, before Jack Cork's match was ended prematurely as the midfielder landed awkwardly on his ankle.
Perhaps destabilised by the enforced change, Saints were forced onto the back foot as Palace enjoyed a spell in the ascendancy.
The hosts had a flurry of corners in quick succession, but the third ended with them falling behind as the set-piece was hoofed away.
It was an unorthodox goal as Rodriguez beat Speroni in a 50-50 challenge before sliding home while sat on the floor.
Jason Puncheon attempted to immediately atone for his mistake, only for his fine cross to be met by a wayward Bolasie effort.
The pacy winger did better by stinging the palms of Boruc in first-half stoppage time, but it was Southampton that went in at the break on top.
Steven Davis threatened and Luke Shaw - fresh from his England debut - stung the palms of Speroni either side of a fine effort from Lambert, who made the most of Palace's inability to clear an Adam Lallana cross and flicked the ball with the outside of his right foot onto the post.
Palace attempted to make amends for the visitors' missed opportunities as they returned for the second half rejuvenated.
Bolasie was proving a handful and, having darted past two Saints players, was brought down by a poor Lovren tackle when through on goal.
The Palace fans called for the Croatia international to be sent off, but Webb did not deem him the last man so only produced a yellow card.
Lovren joined fellow centre-back Jose Fonte in the referee's notebook, which soon also included Davis and Palace captain Jedinak as tempers began to fray.
The latter's foul allowed Lambert to come close with a 25-yard free-kick, which came shortly after Murray saw penalty appeals waved away at the other end.
Morgan Schneiderlin was booked for a lunge on Jedinak as the visitors looked to maintain their lead, with Nathaniel Clyne, making his first appearance at Selhurst Park since leaving Palace, clearing a dangerous cross from substitute Cameron Jerome.
Lovren hacked away a Joe Ledley cross as Jerome loitered with intent and Shaw tested Speroni as the match entered the final 15 minutes.
Palace desperately search for a leveller but, aside from Boruc gathering a looping header from the offside Jerome and Clyne being booked, there was little to report as Saints held firm.