Söderling took the first set 6-4 and fought back from 2-4 down to clinch the second 6-4. But his grass specialist opponent hit back to take the third 2-6 and it went to a tie-break in the fourth, with Söderling emerging victorious 7-6 (7-5.)
Söderling, who only managed a 57 percent success rate on his first serve and made a number of unforced errors, said afterwards to the BBC, "It was really tough and I played my best tennis when I really needed it."
Söderling now meets Australian Lleyton Hewitt on Thursday. Hewitt won Wimbledon in 2002.
There was disappointment though in the women's singles for Sofia Arvidsson who lost in three sets to Anastasija Jakimova.