Söderling looked to be heading for an upset defeat after losing the opening two sets before digging out a gutsy 6-7 (5/7), 3-6, 7-5, 6-4, 6-4 victory before an enthralled Centre Court.
Söderling had never won a match after trailing by two sets before but insisted he had stayed cool under pressure as 2002 Wimbledon champion Hewitt appeared poised for an upset.
“You just have to take it one point at a time,” Söderling said.
“But I felt that if I could raise my game a little bit I would have a chance.”
Söderling now faces either Australian youngster Bernard Tomic or Russia’s Igor Andreev in the next round.
It was a bitterly disappointing loss for Hewitt, whose world ranking plunged to a 13-year low of 130 earlier this month following a miserable sequence of results.
Yet the pugnacious righthander from Adelaide had looked ready to snap his poor run with a vintage performance to take the opening two sets.
Hewitt rallied from 3-1 down in the first set tie-break to take the first, and then pulled off a diving backhand winner to break and go 5-3 up in the second set before holding to take a 2-0 lead.
But Söderling raised his service game over the next two sets, never giving Hewitt a sniff of a break and leveling to force the fifth set, which he claimed when his Australian opponent was broken in the 10th game.