(Reuters) - Colombia became the first side to book a spot in the Copa America Centenario quarter-finals on Tuesday after beating Paraguay in Pasadena, while the United States kept their hopes of advancing alive by thrashing Costa Rica 4-0.

Colombia's 2-1 win put them top of Group A on six points, with the United States on three and the other two teams on one point each.

After losing their opener 2-0 to Colombia, the United States were in clinical form against the Costa Ricans in Chicago and scored three times in the first half through Clint Dempsey, Jermaine Jones and Bobby Wood.

Substitute Graham Zusi added a fourth in the 86th minute to cap the win and improve the hosts' goal difference.

"It was important for us to get off to an early start," said Dempsey. "Once the second went in and the third we got into a bit of a rhythm."

Dempsey got the first, his 50th international goal, from the penalty spot after Cristian Gamboa was adjudged to have pushed Wood in the box with six minutes gone.

Dempsey was involved in the Americans' second after 36 minutes when his run at the Costa Rica defense saw the ball fall to Jones, who struck a low shot from the edge of the box past the outstretched hand of goalkeeper Patrick Pemberton.

The third goal came five minutes later and once again it was Dempsey who set it up. Wood won the ball in midfield and played a one-two with Dempsey before turning to strike home a low drive from 15 yards out.

Costa Rica, who reached the World Cup quarter-finals in 2014, improved in the second half with captain Bryan Ruiz playing a more influential role, but they were ineffective in the last third of the field.

Ruiz hit the post with a header midway through the second half but Costa Rica lost a fourth goal in the dying moments when Zusi stole the ball in midfield and strode forward before slotting the ball home from 15 yards.

In the second Group A game, played at the Rose Bowl in Pasadena, California, Colombia took a 2-0 lead in the first half but were pushed hard in the second.

Carlos Bacca scored the opener in the 12th minute with a header before James Rodriguez doubled Colombia's lead with a left-foot strike on the half-hour mark.

Paraguay gradually played their way back into the match and hit the woodwork before half-time before forcing David Ospina into a world-class save in the 62nd minute, the Colombia goalkeeper diving full stretch to turn a header around the post.

Paraguay continued to dominate the second half and were rewarded when midfielder Victor Ayala scored with a stunning 30-yard rocket in the 71st minute.

However, they could not force an equalizer and Colombia hung on to take all three points and claim a berth in the next round. Paraguay must now beat the United States on Saturday to have any chance of advancing to the quarters.

(Reporting by Andrew Downie and Andrew Both; Editing by Peter Rutherford)