Roberto Firmino added a second in stoppage time to satisfy the home fans on Merseyside.
The five-times world champions have one more friendly before the tournament, against Austria in Vienna on 10 June.
He came on as a second-half substitute for Brazil in a World Cup tune-up against Croatia in Liverpool on Sunday.
He also sat out training with the national team at Tottenham's London base on Thursday as a precaution.
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"Neymar? He'll start on the bench because he's still recovering, and will come on at half-time because we're preparing as a team", Tite told reporters at a press conference on Saturday.
There was still work to do but Neymar somehow managed to force the ball past goalkeeper Danijel Subasic and in off the cross-bar from the edge of the six-yard area.
Neymar marked his return from injury with the first goal in Brazil's win over Croatia at Anfield.
Brazil captain and No. 9 Gabriel Jesus was not as impressive in the first half of the match, and was replaced by Firmino after an hour.
Despite the looming spectre of the World Cup, now less than two weeks away, the game proved a physical one. It was only through Neymar's introduction that this was addressed.
After a quiet opening, Croatia went close to taking the lead on 15 minutes but Alisson produced a good save to deny Luka Modric from distance.