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Rodallega struck with 12 minutes remaining at the Britannia Stadium to lift Roberto Martinez's side out of the relegation zone on the final day of the season.
It completed a great escape for the Latics, who looked dead and buried when they trailed 2-0 against fellow strugglers West Ham last weekend.
They battled back to win 3-2 in that crucial game and Rodallega's heroics in the Potteries, coupled with Birmingham's defeat at Tottenham and Blackpool's loss at Manchester United, guaranteed another season of Premier League action at the DW Stadium.
Wigan's dramatic survival was in sharp contrast to a dismal first half display, with the visitors looking nervy from the first minute when Ali Al-Habsi had to save from Kenwyne Jones.
Stoke had the ball in the net in the 11th minute when Jones' header from a Rory Delap long throw was helped in by Jonathan Walters, who was well offside.
The beaten FA Cup finalists came even closer on 14 minutes when Jones prodded goalwards from another Delap throw and with Al-Habsi nowhere, Emmerson Boyce cleared off the line.
Al-Habsi redeemed himself with a fine stop from a Jones drive in the 25th minute.
Wigan striker Conor Sammon had scored a crucial goal against West Ham and his first chance came in the 62nd minute when he turned just inside the box and fired a low left-foot shot which was gathered by Asmir Begovic.
But Martinez sought to add new impetus to his strike-force in the 67th minute when he replaced Sammon with Tom Cleverley.
Cleverley had Wigan's best chance with his first touch when he was sent through at a tight angle by Charles N'Zogbia but could only hit a low shot straight at Begovic.
United's third goal against Blackpool shunted the visitors towards safety and Rodallega ensured they took another giant stride with his superb 79th-minute finish.
Rodallega met a Mohamed Diame cross to flick the winner past Begovic and spark wild scenes in front of the visiting supporters in the South Stand.
Urged on by boss Tony Pulis on the touchline, Stoke pushed for an equaliser with Glenn Whelan floating a free-kick inches over Al-Habsi's bar.
Five minutes of added time, which included Al-Habsi spilling a Delap corner, did nothing to settle Wigan nerves before the final whistle ensured the celebrations could begin.
