The unbeaten Americans recorded their fourth straight shutout victory but the tiny Caribbean island of Curacao gave them their biggest test of the tournament so far.
The US looked sluggish in the second half at Lincoln Financial Field Stadium in Philadelphia and needed some superb goalkeeping from Zack Steffen to move on.
They advance to face Jamaica who beat Panama by the same 1-0 score in the other quarter-final on Sunday.
"It wasn't one of our best games but it is about moving on and that's what we did," McKennie.
McKennie scored in the 25th minute, finding open space near the back post and heading home a perfectly-timed cross from teammate Christian Pulisic. McKennie said the play is something they work on in training.
"He (Pulisic) likes to cut in a lot and I like to make late runs into the box," said McKennie.
"I always tell him when he cuts in to look for me around the back post."
Curacao, who were the surprise second place finishers in Group B, controlled most of the play in the second half as they pressed for the equalizer.
Steffen faced more shots on Sunday than the US faced in the entire group stage.
Curacao came close to levelling the score in the 84th minute when Leandro Bacuma weaved around a couple of defenders and aimed his shot for the top corner but Steffan made a desperate stab at the ball and managed to deflect it over the crossbar with his finger tips.
Curacao had the Americans on their heels and for awhile it looked like they might have a chance to follow Haiti, who knocked out Canada, and score a big upset.
"We fought like lions. We did everything to win," said Curacao's Cuco Martina.
Elsewhere, Jamaica moved a step closer to reaching their third straight Gold Cup final as they booked their spot in the semis on Sunday with a 1-0 victory over Panama.
Darren Mattocks converted a penalty in the 75th minute for Jamaica, who won their group but struggled to do so after playing to draws with El Salvador and Curacao.
The Reggae Boyz got a break Sunday when Panama's Michael Amir Murillo was called for a controversial hand ball as he was challenging Mattocks for a header at Lincoln Financial Field.
The Jamaican players then argued over who would take the penalty kick before Mattocks won out. He made no mistake, pushing it into the open side after Panama keeper Luis Mejia guessed wrong.