Reinaldo Rueda's men could have put breathing spaces between themselves and fifth-placed Uruguay ahead of their match against Colombia on Tuesday.
But the hosts, bottom of the group, doggedly ground out a point after substitute Jaime Arrascaita's goal had threatened to hand them a rare win.
Felipe Caicedo's penalty earned the visitors a draw but they will see it as two points dropped.
Ecuador had a 100 per cent record in their eight previous visits to La Paz and would have been hopeful of leaving with a win.
Both teams made a raft of changes from their respective matches on Friday.
Rueda made five to the side that lost 1-0 to Colombia, one was enforced as Gabriel Achilier was suspended for the clash.
Bolivia brought in several new faces, too, including goalkeeper Romel Quinonez, who replaced Sergio Galarza following his error-ridden performance in the 4-0 loss to Paraguay.
The visitors showed plenty of energy early on despite the high altitude in La Paz and had a goal disallowed after 14 minutes.
Manchester United winger Antonio Valencia fired a superb ball across the box, but Jefferson Montero went too far beyond the last man and was flagged offside as he tapped home.
Bolivia found their feet as the half went on and managed to hold onto the ball for longer periods than in the opening quarter.
Juan Arce dragged a shot just wide of Alexander Dominguez's goal just after the half-hour mark to underline their growing threat.
Bolivia got another sight of goal right on half-time. Alejandro Chumacero got behind the Ecuador defence and was about to shoot when Juan Carlos Paredes intervened with a strong challenge.
The second half saw Bolivia take a surprise lead and it was introduction of Arrascaita that made the difference.
He picked up the ball 30 yards out and fired in a speculative effort that squirmed through the hands of Dominguez.
Bolivia could have made it two when another substitute Marcelo Martins set-up Arrascaita, whose header rattled the post.
When Martins hit the bar soon after, it looked as though a second goal for the hosts was imminent.
But they were made to rue the two missed opportunities three minutes later when Ronald Raldes Balcazar tangled with Montero in the area, handing the visitors a penalty.
Caicedo duly scored from the resulting spot-kick to level the scores.
They went in search of a winner but could not find one and their World Cup fate continues to hang in the balance.
