After a see-saw match of high drama the Russians came out 6-4, 4-6, 7-6 (10/8) winners and face Canada, quarter-final victors over Australia, in Saturday’s semi-finals.
Earlier in the day Rublev won the first singles over Filip Krajinovic 6-1, 6-2 to give Russia a lead, cancelled out later by Djokovic, who overcame Khachanov 6-3, 6-3.
In the absence of Daniil Medvedev, the Russian star who pulled out of the event citing exhaustion, Russian captain Shamil Tarpischev placed his faith in Rublev and Khachanov for both singles and doubles.
In the end, all hinged on the doubles with Russia taking an option on victory with a 6-4 first set win.
In the second set and with the Serbs up 4-2 Djokovic appeared to suffer
discomfort from his right elbow, the same place where her reported pain at the ATP Finals last week.
After receiving two massage sessions during change overs he appeared to have recovered and Serbia were back on level terms one set-all.
The third set went to 6-6. Then the Serbs missed three match points in the tie-breaker, most agonisingly when Troicki missed an easy volley for victory.
The Russians made no mistake when their turn came, clinching victory with their first match point.