The Russian won the ATP 250 event on home soil in 2009, but he suffered disappointment in Moscow this time around as Kukushkin - runner-up in 2013 - won their quarter-final showdown 1-6 7-6 (7-5) 6-0.
There was not even a hint of an upset when the seventh seed wrapped up the first set in just 29 minutes, underlining the 47-place gap between the two in the rankings.
But momentum swung in Kukushkin's favour in a long second set that was settled by a tie-break in which the underdog seized on his fourth set-point opportunity.
The contest appeared delicately poised at that point, but world number 74 Kukushkin ran away with it in the decider as the Kazakhstani displayed ruthless efficiency to maintain hopes of just a second singles title.
Kukushkin will meet second seed Marin Cilic in the semis after the Croat's 6-3 6-3 victory over Tommy Robredo.
Cilic, ranked eighth in the world, is enjoying an excellent season, having won his first grand-slam title at the US Open in September.
And he is looking primed to add to his collection of silverware after producing a confident display against his Spanish opponent.
Ernests Gulbis, seeded third, was made to work hard for his last-four spot, but the Latvian held firm to defeat last year's semi-finalist Andreas Seppi 7-6 (8-6) 4-6 7-6 (7-3).
He will now face Roberto Bautista-Agut following the Spaniard's 7-5 6-3 triumph over Ricardas Berankis, conqueror of pre-tournament favourite Milos Raonic in the previous round.