The opening game in World Cup Group E continued the vibrant tone of the tournament so far and Rueda's men struck first in an enthralling encounter.
Enner Valencia made it five goals in his last five international appearances when he headed home Walter Ayovi's free kick but, having benefited from slack Swiss set-piece marking, Ecuador were similarly generous when half-time substitute Admir Mehmedi levelled matters in the 48th minute.
Another attacking substitute had the final say, though, when Ricardo Rodriguez's low cross was turned in from close range by Haris Seferovic in the last seconds of stoppage time.
Seferovic's goal arrived on the counterattack as both teams kept up the match's ferocious intensity, and Rueda felt his team let their hearts rule their heads during the frantic finale.
"This provoked the goal which took the draw away from us. I believe a moment of naivety cost us the match.
"It was an intense and evenly matched game. We've seen both teams perform to the best of their ability. We seemed to have the game under control, but what use is that if you end up losing?
"But that's football, although we didn't deserve to lose. Both teams went looking for the win.
"We have to get this defeat out of our heads and get ready to face two very strong opponents."