Dempsey scored his third goal in as many games for Jurgen Klinsmann’s side at CenturyLink Field, pouncing on 22 minutes before setting up a second for Los Angeles Galaxy forward Gyasi Zardes in the 65th minute.
Michael Arroyo pulled a goal back for Ecuador in the 74th minute to set up a frantic finale, but the US held on and will now face either Argentina or Venezuela in the semi-finals in Houston next week.
But the victory came at a cost for Klinsmann’s side who saw key midfielder Jermaine Jones sent off early in the second half to earn a suspension which will see him miss the semi-final.
France-based midfielder Alejandro Bedoya and Hamburg striker Bobby Wood also earned yellow cards that will see them suspended for the last four.
For Ecuador, Manchester United’s Antonio Valencia was dismissed after picking up two yellow cards before triggering the melee which led to Jones’ dismissal.
Earlier, a cagey start had seen both sides begin tentatively before Jones and Michael Bradley steadily imposed themselves in midfield as the US started to gain the upper hand.
Wood’s speed troubled the Ecuador defense on 17 minutes, when he darted onto a low pass only to prod his finish well wide of the advancing Alexander Dominguez.
– Dempsey strikes –
Yet five minutes later the US took the lead with a beautifully worked goal that began when Dempsey gathered in midfield and released Wood, who fed Jones near the edge of the area.
The midfielder picked out Dempsey with a superb cross and the former Tottenham and Fulham stalwart duly headed home.
Five minutes later Dempsey was threatening again, this time his shot well-saved by Dominguez.
Bedoya almost doubled the US lead three minutes before the break when played through Dempsey, yet Dominguez saved smartly down to his left.
The South Americans had a strong shout for a penalty when Enner Valencia was bundled over by Stoke City’s Geoff Cameron and the West Ham striker also went close with a glancing header in the 48th minute.
Three minutes later the simmering nature of the contest boiled over, when Antonio Valencia, booked for a sly kick on John Brooks in the first half, picked up a second yellow for clattering into Bedoya.
In the skirmish that followed Jermaine Jones appeared to flick Valencia in the face with a hand and earned a straight red from Colombian referee Wilmar Roldan.
With both sides down to 10 the game opened up dramatically but it was to be the US who struck first.
Dempsey latched onto a long ball forward and showed great determination to cut back for Zardes who had the easiest of tap-ins at the far post for 2-0.
Ecuador responded furiously, pulling a goal back through Michael Arroyo’s thunderous low strike in the 74th minute.
Enner Valencia had hearts in American mouths two minutes later when he headed wide from close range.
Ecuador laid siege to the US goal and in a frantic finish saw manager Gustavo Quinteros given a red card from the touchline.