The team, and country, had further cause for celebration when Veerpalu's compatriot Jaak Mae took the bronze medal.
Norway's Frode Estil finished second.
Veerpalu, a strong classical-style racer, led the race throughout and crossed the line in 37 minutes 07.4 seconds - 36 seconds ahead of Estil.
"I hoped it would be gold and at the halfway point I knew I would win," the 31-year-old said.
"I had good control pretty much throughout the race, but I feared the Norwegians."
Veerpalu came into the Games after a strong performance in the World Championships last year where he won the 30K classical race and just missed the podium with a fifth in the 15K classical.
Estil's silver capped a great day for Norway on Soldier Holow's trails.
Earlier in the day, fellow Norwegian Bente Skari won the women's 10K classic race.
"I'm really happy with the medal and my race," Estil said.
"The distance to Veerpalu was so big that I concentrated on winning the silver."
Norway's Anders Aukland was fourth with Sweden's two-time world champion Per Elofsson in fifth.