Coming into the stadium at the end of the 10-km track, Frenzel was neck and neck with Japan's Akito Watabe. The 25-year-old world number one pulled away powerfully some 300 metres from the finish to win by 4.2 seconds.
"I knew I was stronger in the sprint. That's my advantage over Akito," Frenzel told a news conference.
The two men jumped the furthest from the normal hill and started about 30 seconds ahead of the pack on the cross-country leg. They were never threatened on a course that organisers had salted heavily to compensate for temperatures of 12 Celsius (54 Fahrenheit) at the start of the race.
Frenzel, who is a member of Germany's armed forces, raised his arms in triumph as he slid across the line in 23 minutes 50.2 seconds.
It was the first Olympic gold for the German, who is the world champion on the large hill. He won a bronze in the team event at the 2010 Games.
Watabe, the world number two, was never more than two seconds ahead of his rival on the track.
"He is really strong on the jumping hill and also the cross-country track and the final sprint," Watabe told reporters. "I think he is perfect, one of the best Nordic Combined athletes ever."
Watabe's medal was the first Japan had won in the event since taking team gold in 1994.
Magnus Krog of Norway, who started the cross-country section more than a minute behind Frenzel, skied the second fastest cross-country leg to win the bronze. He finished 8.1 seconds behind the German.
Rather than skiing a 10-km course, athletes at Rosa Khutor travel four times around a 2.5-km track. Frenzel and Krog said the course had been in relatively good condition, given the warmth.
Frenzel landed the longest jump of the day, soaring 103 metres. Watabe came second with a leap of 100.5 metres to start six seconds behind the German.
Young Russian athlete Evgeniy Klimov raised the hopes of the noisy home crowd by coming third in the jumping session. But he had a terrible time on the track and finished last overall.
Defending champion Jason Lamy Chappuis of France, who was eighth in the jump and started 31 seconds behind Frenzel, ended in 35th place after struggling on the course.
Lamy Chappuis, who also won the normal hill title at last year's world championships, blamed a bad choice of skis.
U.S. athletes had little luck on a cross-country section they traditionally favour. Bill Demong, who won the large hill event in 2010, finished in 24th place.