This is the 14th time this season that the Swede has reached a quarter-final and he took 61 minutes to defeat 59th ranked Gimeno-Traver 6-2, 6-3, who had no response to Söderling's power.
Gimeno-Traver produced an unexpected win over Nicolás Almagro in the last round, but with the scores at 1-1 in the first set, he went on to be broken twice by the world number five and lost the first set 6-2.
Söderling continued relentlessly in the second and Gimeno-Traver, always on the back foot, lost his serve twice again, sealing his exit.
Fourth seed David Ferrer, also of Valencia, is also looking strong after beating Russian qualifier Teymuraz Gabashvili 6-4, 6-1. Ferrer, who has been a runner-up in three tournaments this season as well as a semi-finalist at the US Open, was the clear favourite and broke early on in the first set.
Gabashvili refused to roll over, but the Spaniard always had the edge. It was a different story in the second, as Ferrer raced to a four-game lead before winning 6-1.
Russia's Nikolay Davydenko came to Valencia determined to produce a good display after dropping out of the world top 10 just over two weeks ago.
He started the season well, winning in Doha in January -- where he beat world number one Rafael Nadal in the final -- but he then fractured his wrist in a semi-final defeat by Soderling in Rotterdam and his form has dropped.
Davydenko had an easy first-round win over wild-card entry Javier Marti, which meant a tough tie against Argentine Juan Ignacio Chela, who had beaten him six times in their seven previous meetings.
Both players were guilty of unforced errors and the first set saw five consecutive breaks of serve before Davydenko cruised to 7-0 in the tie-break.
Chela, ranked 40, has been playing well, winning in Bucharest at the end of September, but as Davydenko began to find his rhythm, he had no response and was broken twice in the next set to lose 6-2.
Later, France's Gael Monfils, a winner in Montpellier last week, takes on Stanislav Wawrinka of Switzerland as he looks to qualify for his 11th tour-level quarter-final of the season.