"I was trying to save the tyres because you don't pit for a change during the sprint race. I was hoping the performance wouldn't drop off."
Evans shadowed Stephane Richelmi for 15 laps before his pressure finally paid off with six laps to the finish.
Richelmi ran wide and Evans slipped through into third.
"I'd saved my tyres to have a crack at him. I could see he was struggling and then he made a little mistake and I was through.
"The car was a lot better than it was in the Saturday race. My Arden team did a great job."
Three-time defending champion Sebastian Vettel held off Red Bull teammate Mark Webber in a scintillating battle to win the Malaysian Grand Prix last night.
Vettel, who earlier in the race complained to the team about Webber's slow pace, battled the Australian for much of the race, with the cars almost touching as the German grabbed the lead on the 46th lap for his 27th victory.
Lewis Hamilton was third ahead of Mercedes teammate Nico Rosberg.
It was a disastrous day for Ferrari's Fernando Alonso, who crashed out of the race on the second lap.