The second-seeded Troicki saved all three break points he faced to beat Denis Istomin, of Uzbekistan, 6-1 6-4 in his opening match, thereby avenging defeat in their only previous meeting.
"The first set I played pretty good, controlling that part of the match," Troicki told www.atpworldtour.com.
"The second set was pretty equal. I was just a bit more focused at the end to make a break to win the match. I'm happy to be in the quarter-finals."
Troicki will meet seventh-seeded Russian Dmitry Tursunov tomorrow for a place in the semi-finals.
Fifth seed Nikolay Davydenko had to battle hard to defeat Poland's Lukasz Kubot 6-3 7-6 in their first meeting since January 2006 at the Australian Open.
Davydenko, the inaugural champion in 2009, trailed 5-2 in the second set but fought back to set up a tie-break which he won 7-2.
"At 5-2 down in the second set, I was already thinking about the third set," said Davydenko. "I was just fighting for the points and was able to come back and win it in two sets. Sometimes it happens that way."
Also through to the last eight are Japan's eighth seed Kei Nishikori and top seed Nicolas Almagro.
Germany's Philipp Petzschner saved two match points before going down 6-3 4-6 7-5 to Nishikori while Almagro needed two tie-breaks to get the better of fellow Spaniard Albert Ramos.
Almagro double-faulted to give Ramos a set point but held his nerve to set up a tie-break and never looked back after racing into a 5-1 lead, eventually prevailing 7-2. He then won the second-set tie-break 7-4.