Rodrygo's deflected 30th-minute strike was enough to secure all three points for Brazil, who were languishing in sixth place in the South American qualifying standings before Friday's result in Curitiba.
The five-time World Cup winners moved up to fourth place with 10 points from seven games after their third win of the qualifying campaign, but remain eight points adrift of leaders Argentina.
With the 2026 World Cup in the United States, Canada and Mexico expanded to include 48 teams, the top six finishers in South American qualifying will be guaranteed a place at the tournament. The seventh placed South American team enters an inter-confederation play-off.
Brazil have struggled in recent international tournaments, losing in the quarter-finals of the 2022 World Cup and failing to progress past the last eight at this year's Copa America.
The lack of fluency that has characterised their recent form was back in evidence against Ecuador on Friday, where despite dominating possession for long periods they created little in the way of clear-cut scoring chances, with only three shots on goal.
The breakthrough came on the half-hour mark, when Rodrygo collected the ball on the edge of the area, took a touch and then shot from 25 yards. The Real Madrid attacker's strike appeared to clip Ecuador defender Willian Pacho before flying in off the post.
Frustrating farewell
In other South American qualifiers on Friday, Luis Suarez bade a frustrating farewell to international football as Uruguay were held to a 0-0 draw by Paraguay in Montevideo.
Suarez, 37, announced on Monday he was stepping down from international duty after a glittering 17-year career for Uruguay that saw him finish as the country's top scorer with 69 goals from 143 appearances.
Suarez was feted in a pre-game ceremony which saw him gathered on the field with his family to receive tributes from fans, as well as a video message of congratulations from close friend Lionel Messi.
"Uruguay is bigger than any player. Starting tomorrow I will be another fan," an emotional Suarez told fans in an address to the stadium.
But the former Barcelona and Liverpool star, who now plays in Major League Soccer with Inter Miami, was unable to add a 70th goal to his international tally in Friday's farewell game at the Estadio Centenario in Montevideo.
Despite enjoying 65% possession, Uruguay were unable to find a way through a dogged Paraguay defence in a disjointed match littered with some 24 fouls.
Suarez, whose career at international and club level was dogged by controversies such as his ban for biting Italy's Giorgio Chiellini at the 2014 World Cup, was one of four Uruguay players to be shown a yellow card in a fractious encounter.
The result left Uruguay in second place in the standings with 14 points from seven games, four points behind leaders Argentina.
In Friday's other qualifying game, third-placed Colombia needed a late goal from Liverpool's Luis Diaz to salvage a 1-1 draw with Peru in Lima.
Alexander Callens had fired Peru into a shock lead on 68 minutes, but Diaz headed in from close range eight minutes from time to give Colombia a share of the points.
The result leaves Colombia in third place in the standings with 13 points from seven games.
