Latvian Gulbis was handed a bye in round one but was taken the distance in a gripping encounter with Philipp Petzschner in their second-round clash at the ATP 250 hard-court event in Kuala Lumpur.
Eventually, though, Gulbis came through 6-3 6-7 (3-7) 6-1 to ensure his spot in the last eight.
Gulbis' cause was helped by landing 15 aces and winning 81 per cent of first-serve points. However, the 26-year-old, who had lost to Petzschner in their only other encounter in Marseille in 2011, made life difficult for himself by landing just 59 per cent of first serves.
The world number 13 battled through, though, wrapping up the decider with relative ease and he will now meet Benjamin Becker for the right to contest the semi-finals after the German defeated Pierre-Hugues Herbert 6-4 7-6 (7-4).
Third seed Mayer saw his participation end at the second round, however, as Finn Jarkko Nieminen produced a shock 7-6 (7-5) 6-4 success.
Nieminen had not reached an ATP Tour quarter-final since February but won back-to-back Tour level matches for first time since June in a time of one hour and 40 minutes.
Next up for Nieminen is a last-eight match with seventh seed Pablo Andujar after he prevailed 6-4 6-7 (6-8) 6-3 against Michal Przysiezny.