The 44th-ranked, 34-year-old Stepanek beat the 23-year-old Lajovic, world number 117, 6-3, 6-1, 6-1 in under two hours, handing the Czechs an overall 3-2 win.
On the hardcourt of the Belgrade Arena, the Czech Republic, playing the third Davis Cup final in five years, scored a ninth straight victory in Davis Cup ties.
"I was under the biggest pressure that can be," said a jubilant Stepanek. "We are one of only five teams that have defended the cup."
"I want to say how proud I am to be with these lads. They are absolutely great, they deserved to win the trophy," said interim Czech captain Vladimir Safarik, who replaced an ill Jaroslav Navratil for the final.
His counterpart Bogdan Obradovic admitted that his emotions were "mixed" as 2010 champions Serbia "tried to do our best" despite being weakened considerably.
Lajovic replaced 36th-ranked Janko Tipsarevic, out with a heel injury, and Serbia also missed 76th-ranked Viktor Troicki over a doping ban.
Lajovic, who has lost all four ATP-level matches he has played this year, started the decisive rubber in high spirits, breaking Stepanek's very first serve.
But his enthusiasm was short-lived as the Czech veteran, betting on patience and changing the rhythm of his play at will, broke Lajovic's next two serves to win the set.
Clad in his lucky blue t-shirt emblazoned with a lion design -- which Andy Murray's mother Judy described as "staggeringly bad" on Saturday -- Stepanek raced to take the next two sets in style.
Casting desperate looks around him, Lajovic let his game crumble and allowed Stepanek to enjoy the ovations from a noisy group of Czechs in the sold-out arena.
"I controlled the rubber except in the first game, and I played in the best form of my life the whole weekend," said Stepanek.
Lajovic admitted he found it hard to predict Stepanek's moves.
"I think it was his biggest advantage in this match."
Earlier, Serbia's world number two Novak Djokovic forced the decisive rubber as he beat seventh-ranked Tomas Berdych 6-4, 7-6 (7/5), 6-2 for his 24th victory in a row.
Propelled by a noisy home crowd, Djokovic relied on his serve, while Berdych tried to indulge him in long exchanges, combining a fast forehand with a wicked sliced backhand.
"It was very emotional, both of us got into the match with a lot of pressure because of the importance of the game," Djokovic said.
Djokovic earned ten break points against none for Berdych in the first set and finally converted his fourth set point for a 6-4 lead.
He went on to take the second set in tie-break after letting off some steam and destroying a racquet, and before taking the third set in style, 6-2.
Berdych admitted that Djokovic's victory was deserved.
"I tried to hold on to him from the beginning to the end but it wasn't enough," he said.
"He's in an excellent shape, he plays great tennis and moreover in front of such a crowd."
In Friday's singles, Djokovic beat Stepanek 7-5, 6-1, 6-4, and Berdych then saw off Lajovic 6-3, 6-4, 6-3.
On Saturday, Berdych and Stepanek won the 14th of their 15 Davis Cup doubles rubbers together as they swept Ilija Bozoljac and Nenad Zimonjic 6-2, 6-4, 7-6 (7/4).
A year ago, the Czechs beat Spain 3-2 in Prague for their first triumph as an independent country with Stepanek again winning the decisive final rubber.
Former Czechoslovakia, which split into the Czech Republic and Slovakia in 1993, won the cup in 1980.
Photos: SRK does garba, Nawazuddin takes 'shower' in bathtub
Photos: Soha Ali Khan, Evelyn Sharma, Urvashi Rautela at Mumbai airport
Spotted: Lara Dutta, Mahesh Bhupathi with their daughter in Bandra
Photos: SRK, Tamannaah Bhatia, Varun Dhawan at Mehboob Studio
Birthday special: Sushant Singh Rajput's journey from TV to films