1245 GMT November 21, 2019
Morales had 45 percent of the vote to Mesa's 38 percent, the Supreme Electoral Tribunal announced, with most of the votes counted, AFP wrote.
Elected Bolivia's first indigenous president in 2005, Morales has won his previous elections in the first round, never having to contest a runoff.
The former coca farmer and leftist union leader has led the poor but resource-rich Latin American country for the past 13 years.
He will face a stiff challenge from Mesa, a 66-year-old former president who led Bolivia from 2001-2005.
Mesa celebrated "an unquestionable triumph" in getting to the second round, amid cheers from his supporters at his La Paz headquarters.
Morales welcomed his first-round win, telling cheering crowds "we have won again, really, it is something historical, unforgettable."
South Korean-born evangelical pastor, Chi Hyun Chung, was the surprise package of the election, polling strongly to finish in third place with 8.7 percent.
His support is likely to be influential during campaigning for the second round on December 15.
Morales obtained Constitutional Court permission in 2017 to run again for president even though the constitution allows only two consecutive terms.
A new mandate would keep him in power until 2025.
Milton Quispe, a student, said he would vote for "Evo, because he has taken care of the poor. He has known how to give us dignity."
Bolivia's seven million eligible voters also cast ballots to choose members of the 166-seat Congress – 36 senators and 130 deputies.
After voting in his coca-growing district of Chapare, Morales, a member of the Aymara indigenous community, said he was optimistic about his chances and confident in Bolivia's democracy.
As leader of his Movement for Socialism Party (MAS), Morales points to a decade of economic stability and considerable industrialization as his achievements, while insisting he has brought "dignity" to Bolivia's indigenous population, the largest in Latin America.