Cibulkova beat Safina 6-7 (3), 6-1, 6-4 Friday to give Slovakia a 1-0 lead and hand Safina her first singles loss of the tournament. Hrbaty then beat Safin, 6-7 (5), 7-5, 7-6 (3) to clinch the championship before about 8,000 people at the Burswood Dome.
Each team had 3-0 records going into the final and led their groups in round-robin play.
It was Slovakia's third title in the 21-year history of the Hopman Cup. Hrbaty won the mixed teams event in 2005 with Daniela Hantuchova.
Safina, who defeated Alize Cornet of France, Italy's Flavia Pennetta and Hsieh Su-wei of Taiwan in the group stages, gave away three set points in the 10th game of the opening set.
Trailing 5-1 in the deciding set, Safina won the next three games, but Cibulkova held her serve in the final game to take the match. It was the Slovakian's first win over Safina in three career matches.
"I was up 5-1 and suddenly it was 5-4, then she had a break point so I was really fighting,'' Cibulkova said. "I'm just so happy I beat her. I had to play aggressive.''
Safin, who was unusually subdued during his group matches, displayed his typical volatility in the final, smashing a racket in the first set.
But the 28-year-old Safin, who has said he will retire at the end of 2009, also entertained the crowd. During a tense moment in the third set, with Hrbaty struggling to hold serve, Safin gave the net judge a kiss on the cheek after his wayward forehand hit her in the body.
Slovakia ousts Australia, Italy beats France
David Silva To Return For Valencia This Week
Russia, Slovakia in Hopman Cup final
