McAnuff slotted home past Esteban Alvardo in the 48th minute to earn Jamaica an unexpected point against Costa Rica, who are CONCACAF'S top team in the FIFA world rankings at 14.
Jamaica, ranked 65th, had also grabbed a surprise lead in the 13th minute through Garath McCleary before Costa Rica, Gold Cup runners-up in 2002, stormed back with two goals in four minutes at StubHub stadium.
Roy Miller got his head on a cross to equalise in the 33rd minute and David Ramirez then put the 'Ticos' ahead.
In the day's other Group B game at the same venue, Canada and El Salvador played out a drab 0-0 draw.
El Salvador were the more dangerous side throughout but it was Canada who produced the best scoring chance late in the opening half.
Cyle Larin broke in on goal, dribbled around the goalkeeper and with the goal at his mercy drove the ball high and wide.
The Gold Cup determines the regional champions for North and Central America and the Caribbean.
(Reporting by Steve Keating in Toronto; Editing by Peter Rutherford)
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