Safarova won the second reverse singles for an unassailable 3-1 lead in the final of the best-of-five series. Jankovic, a former No. 1 player, was slowed by a back injury and was in tears afterward.
The winning point came on Safarova's forehand on her second match point on the hard court at O2 Arena. As the Czech players danced, the ecstatic, sell-out crowd celebrated with the wave.
"It's hard to describe how I feel. I played an unbelievable game," Safarova said. "I desperately wanted to win and I'm really delighted. It's fantastic to win at home, in Prague. I played one of the best matches of my career."
The Czechs are the third country in a row to successfully defend the Fed Cup title. Russia won the top prize in women's team tennis in 2007-08 and Italy 2009-10.
The Czechs took a 2-0 lead after the opening singles Saturday, but Ana Ivanovic made it 2-1 Sunday by beating Petra Kvitova 6-3, 7-5. It was the first loss for Kvitova after 11 straight Fed Cup singles wins.
The 17th-ranked Safarova saved two break points before racing to a 4-0 lead in the first set, and broke Jankovic twice in the second to open a 5-1 advantage. Jankovic was treated between sets for a back injury.
"I'm really very sorry for my team that I wasn't able to be at 100 percent today," Jankovic said, unable to hold back tears. "I tried my best on the court but it wasn't good enough. I wasn't able to move properly. Throughout the match, it was getting worse and worse."
In the first reverse singles, Ivanovic defeated Kvitova, who recovered just in time from the bronchitis that forced her to withdraw from last week's WTA Championships.
The Czechs won their first title last year since Czechoslovakia's split in 1993. Czechoslovakia won five times, including three straight from 1983-85.
"Lucie needs to bottle this feeling and play like this at regular tournaments! A hero is born," tweeted Martina Navratilova, who won the Fed Cup with Czechoslovakia and later the United States.
"I don't feel like a hero," Safarova said. "It's a team competition. We all contributed."
Despite the loss, Serbia has enjoyed its best Fed Cup season as an independent nation. It recorded its first victories in the World Group with away wins over Belgium and Russia to reach its first final.