Playing his first competitive international since being banned for biting Giorgio Chiellini in the 2014 World Cup Finals, Suarez, along with striking partner Edinson Cavani, dragged Uruguay back into the game after they went 2-0 down after 25 minutes.
"As always, we showed character," the Barcelona striker said after the game.
Playing in front of a capacity crowd at the Pernambuco arena, Brazil took the lead after just 39 seconds thanks to Douglas Costa.
Willian whipped a cross in from the left and the Bayern Munich striker nipped in between two defenders to poke the ball home with the sole of his boot.
Brazil got a second 24 minutes later thanks to Renato Augusto. Defender Mauricio Victorino could not quite cut out a long pass from Neymar and the loose ball fell to the Beijing Guoan midfielder who wrong-footed the goalkeeper with a sublime dummy and knocked the ball into the empty net.
The home side were dominating the game but Uruguay got back into the match after 31 minutes when Carlos Sanchez headed a ball down to Cavani and the Paris St Germain striker hammered home from 10 yards out.
Uruguay came out for the second half looking the hungrier of the two sides and Suarez got the equaliser with the help of slack marking by David Luiz.
Luiz stood off the striker and allowed him to fire home an angled drive that Alisson got a hand to but could not save.
Suarez, who was booked for stamping, almost grabbed a winner with five minutes to go when a loose header from Luiz left him free on goal but Alisson got down well to save with his feet.
"I think that when we were winning 2-0 we had the game in the hand but we let them get back in the game," Renato Augusto told reporters.
"And when they scored they closed us down and played on the counter attack. Our big mistake was conceding the first goal."
The result means Uruguay retain second place in the 10-team South American qualifying group three points behind Ecuador, who lead with 13 points.
Brazil are in third place with eight points.
The top four teams qualify for Russia 2018 and the fifth place side go into an intercontinental play off.
Brazil now go to Asuncion to face Paraguay on Tuesday, and will be without captain Neymar, who was booked. Uruguay will be at home to Peru.
(Editing by Sudipto Ganguly)
