(Reuters) - Carlos Bacca's first-half goal was enough to give Colombia a 1-0 victory over the United States in the third-place playoff at the Centenary Copa America in Arizona on Saturday.

The winning goal came after half an hour when Colombia forged a well-worked move down the right with Juan Cuadrado slipping the ball inside to James Rodriguez, who chipped forward for Santiago Arias to head across goal for Bacca to slide home.

Colombia finished third, their highest finish since 2001, while the host nation took fourth place, matching their best ever finish in the tournament.

The title will be decided on Sunday when favorites Argentina take on defending champions Chile in New Jersey.

The third-place playoff is traditionally an opportunity for teams to give their second string players a chance to shine but neither coach made widespread changes as they went all-out for the win at the University of Phoenix Stadium in Glendale.

The first half was poor, with Bacca's goal giving Colombia a deserved lead at the break, but things perked up in the second half as the host nation pressed for an equalizer and their first win over Colombia in four Copa clashes.

Clint Dempsey had a beautiful free kick tipped over by David Ospina after 51 minutes and then both sides hit the woodwork in a matter of seconds.

Cuadrado's deft chip from outside the box was unlucky to bounce down off the bar and back into play and then Bobby Wood smacked the post with a crisp shot at the other end.

The U.S. enjoyed a bulk of the possession in the second period but rarely threatened Ospina as they struggled to convert their territorial advantage into shots on target.

The match did come to a boil with two minutes remaining, however, when Colombian right back Arias brushed his head against Michael Orozco, who retaliated with a push in the face and both men were sent off.

"We had good chances and we played well," U.S. keeper Tim Howard said in a pitchside interview. "But I think there are no excuses."

(Writing by Andrew Downie; Editing by John O'Brien)