Ecuador had not lost to Bolivia in the tournament since 1949 but they were soon trailing as Bolivia launched an opening blitz in the Group A match.
Bolivian captain Ronald Raldes got the first in five minutes when he stooped to head home a corner kick from Martin Smedberg-Dalence, who doubled the lead 13 minutes later when he side-footed home from 25 yards out.
Ecuador should have pulled a goal back from the penalty spot after 38 minutes but Enner Valencia had his kick saved at the second attempt after the referee order his first to be retaken when a Bolivian player encroached into the 18-yard box.
Marcelo Martins made no such mistake at the other end five minutes later when Bolivia were awarded a penalty for dangerous play.
With a strong wind behind them in the second half Ecuador stormed forward and got a goal back in the 47th-minute when West Ham striker Enner Valencia had a simple tap in.
Miler Bolanos narrowed the deficit with a fierce 35-yard drive in the 81st minute and although they kept pressing, with Christian Noboa hitting the bar with six minutes to go, Bolivian goalkeeper Romel Quinonez was in fine form and able to preserve his side's lead.
The win was Bolivia's first in the Copa America since 1997 and takes them to the top of Group A with four points following last week's 0-0 draw with Mexico.
Chile, who beat Ecuador 2-0 in the tournament opener, play Mexico later on Monday.
(Writing by Andrew Downie; Editing by Greg Stutchbury)
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