The 37-year-old champion twice put down the Germany-based Cuban defector, in the seventh and ninth rounds, before the referee Daniel Van de Wiele stopped the fight with 1 minute, 11 seconds remaining in the round.
Klitschko (37-2, 36 KOs) was making the first defense of the title he reclaimed by stopping Samuel Peter in dominating fashion last October. The Ukrainian, whose brother Wladimir holds two other versions of the title, hasn't lost since getting knocked out by Lennox Lewis in 2003.
"I knew that he was a world-class boxer," Klitschko said. "I said before that the fight would not be easy."
At 6-foot-7, Klitschko had a size advantage of more than 3 inches and 19 pounds against his southpaw opponent, who tired in the middle rounds and eventually couldn't move fast enough to get inside of Klitschko's long reach.
The 35-year-old Gomez was the mandatory challenger and Klitschko's former sparring partner, and was trying to become the first heavyweight champion from Cuba.
Gomez managed to frustrate the champion early, keeping his hands high to fend off jabs and peppering Klitschko with right hands.
Klitschko landed his first big right midway through the second round, drawing a smile from Gomez, who showed he could push the bigger man back when he landed a few combinations.
The champion found success leading with his right in the fourth as he began to take control, and opened a small cut on Gomez's right eyebrow in the fifth.
A cut opened high on Klitchsko's forehead in the sixth, and he was forced to backpedal to the ropes in the seventh. But that effort seemed to tire the Cuban, who lowered his hands and provided a better target for Klitchsko, who dropped Gomez to a knee for a count of eight.
Gomez was trapped in the corner and took another big right, and the challenger pulled both fighters to the ground before ending the round defending himself in his own corner.
Gomez got some breathing space in the ninth when Klitschko was reprimanded for gouging, but Klitschko just launched into another assault, downing Gomez by the ropes with another right and finishing the fight a minute later.
"I was a little hectic," Klitschko said. "I wanted to end the fight earlier but I didn't get to hit him enough."
Klitschko said he wants to meet Russian giant Nikolai Valuev, who holds the WBA title, but his next battle might well be in the court room.
Klitschko has appealed to the Court of Arbitration for Sport in Switzerland, which will decided whether the WBC can force him into another mandatory defense against Russian former champion Oleg Maskaev.
Wladimir, who was in his brother's corner, holds the IBF and WBO versions of the heavyweight title and the Klitschkos have long talked about rounding up all the belts between them.
Wladimir Klitschko is in negotiations to face Britain's David Haye, the charismatic former cruiserweight champion, on June 20.
A three-time champion, Vitali retired because of injuries and vacated the WBC belt in 2005, only to return last October and reclaim when Peter decided not to come back for the ninth round.
Gomez previously held the WBC cruiserweight title for four years before vacating in 2002 to move up to heavyweight. He earned the right to face Klitschko by winning a unanimous decision over Vladimir Virchis last September.
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