Wondolowski continued his red-hot form for the American national team with two superbly taken goals in the second half to clinch an expected win after Cuba had grabbed a surprise lead.
Jose Ciprian Alfonso had put the visitors ahead at Rio Tinto Stadium in Sandy, Utah with a 35th minute goal against the run of play but the U.S. dominated the remainder of the match.
The Americans, who thumped Belize 6-1 in their previous Group C match, got back on level terms when Landon Donovan converted a penalty in stoppage time at the end of the first half.
Joe Corona gave the Americans the lead when he scored his first international goal after 56 minutes before Wondolowski banged in two more to lift his tally for the tournament to five following his hat-trick against Belize.
The victory gave the U.S. a maximum six points from two matches and ensured they would advance to the quarter-finals regardless of the outcome of their final match with Costa Rica.
Costa Rica, who beat Cuba 3-0 in their first match, were playing Belize later on Saturday needing a win to also secure their spot in the quarters with a match to spare.
(Reporting by Julian Linden; Editing by Gene Cherry)