Felix Torres' header on 75 minutes cancelled out an early Casemiro strike, while Colombian referee Wilmar Roldan had the red card out three times in the first 26 minutes but the Liverpool goalkeeper's -- awarded for high foot -- was downgraded to a yellow card after consultation with the Video Assistant referee (VAR).
Firstly, on 15 minutes, Ecuador goalkeeper Alexander Dominguez was red carded after 15 minutes for a reckless challenge, and Brazil full-back Emerson Royal was dismissed five minutes later for a second yellow card following a clumsy tackle.
Alisson's second red card was initially handed out in stoppage time but again overturned by VAR. Speaking after the match, he told reporters: "This has never happened to me before. It's the first time.
"I am happy for VAR, it is worth highlighting the use of VAR in football. If there was no VAR, today we would be unfairly penalised for several situations on the pitch. I touched the ball, that's evident to everyone. Both balls were inside my action. In both situations I was aiming for the ball."
Ecuador will feel aggrieved at having a goal chalked off and two penalty awards rescinded by the VAR - including one in second-half stoppage time - but they got just reward for their resilience when Torres headed home from a corner.
Casemiro had put Brazil ahead after five minutes when he hammered home from close range after a goalmouth scramble.
Five-times world champions Brazil have already qualified for this year's finals in Qatar along with Argentina, who beat Chile 2-1 on Thursday. Ecuador are third in the 10-nation South American qualifying standings with 24 points from 15 games.
Ecuador's match against Brazil ebbed and flowed but was enthralling throughout, especially in the opening half hour.
Already a goal down, Ecuador's keeper Dominguez was shown a red card for a neck-high challenge that felled Matheus Cunha on the edge of the box.
But moments later the numbers were even as Brazil's Emerson Royal, who was shown a yellow card in the first minute for a firm challenge, got a second for a clumsy intervention.
Ecuador, on a home pitch where they had earned 16 of their 23 points ahead of Thursday's match, thought they might snatch all three points when they were awarded a stoppage-time penalty.
Alisson felled Ayrton Preciado in attempting to punch the ball clear and was again shown a red card, but after consulting VAR the referee overturned both the penalty award and red card.
The draw saw Brazil extend their unbeaten run in World Cup qualifiers to 31 games to match the South American record they set from 1954 to 1993.
Meanwhile, Uruguay moved into fourth with 19 points after beating Paraguay 1-0 in Asuncion, Luis Suarez getting the winner five minutes into the second half to give new coach Diego Alonso a winning start.
The result keeps Uruguay's qualification hopes alive and dealt a heavy blow to Paraguay, who sit second bottom of the table with 13 points.
Bottom side Venezuela are the only team out of the running to qualify for Qatar, with most sides having four games left to play.
The top four qualify automatically for the World Cup while the fifth-placed side go into a playoff with a team from the Asian confederation.