The Swans twice came from behind to secure the win at the DW Stadium as second-half goals from Rangel, Itay Shechter and Dwight Tiendalli overturned Roger Espinoza and James McCarthy’s strikes for Wigan.
The defeat comes as a huge blow to the Latics, who are three points from safety with two games left to play.
Swansea’s win cements their place in the top half of the table but Rangel, who was signed in 2007 by Roberto Martínez during his time at the Liberty Stadium, does not want to see his former manager’s club relegated.
“I don’t Roberto to go down to the Championship,” Rangel told Sky Sports.
“For them it was a vital game but there are still two games left and hopefully they stay up. But I think about our team and it’s a great three points for us.
“It was important because we had a run of bad results – seven games without a win – and today it was important to get three points to at least secure a top-10 finish.
“We showed very good character and it was a well-deserved three points.”