Bolivia continued to control the match, and doubled their lead when Smedberg curled a first-time effort into the corner from outside the box.
Minutes later, it was Bolivia who were given a penalty after a high boot in the box, and Martins Moreno coolly slotted home to put the game almost beyond doubt.
After the break, Ecuador reduced the deficit thanks to Valencia, who had a simple tap-in after Jefferson Montero split open the defence.
With under 10 minutes to go, Miller Bolanos scored with a scintillating 30-yard strike to give Ecuador hope.
Christian Noboa then rattled the bar as Ecuador searched for an equaliser, and Bolivia held on to make it four points from their opening two matches, topping Group A in the process.