The Seattle Sounders star was on hand to convert Gyasi Zardes’ pinpoint low delivery after 27 minutes to give his side a deserved lead but they had to work hard to see out a narrow win as DeAndre Yedlin was sent off just after half-time.

Yedlin received two yellow cards in the space of a minute, leaving his team a man short for the majority of the second half, but they clung on to book their place in the last eight.

The host nation may yet avoid a tough quarter-final clash with Brazil as Colombia suffered a shock 3-2 loss at the hands of already-eliminated Costa Rica at the NRG Stadium in Houston.

The victory for Costa Rica, who reached the last eight of the 2014 World Cup, saw the Americans progress as Group A winners and the Brazilians are expected to follow suit in Group B, meaning the two sides would not face each other in the last eight.

The clash between the US and Paraguay began at a frantic pace and the South American outfit could have edged ahead early on but John Brooks’ perfectly-timed challenge denied Miguel Almirón.

They were made to pay for not being more clinical in front of goal just before the half-hour mark as Zardes beat his man before crossing for Dempsey, who was in the right place at the right time, sweeping a shot beyond Paraguayan goalkeeper Justo Villar to put the US in front.

Brad Guzan was by far the busiest of the two goalkeepers and was forced into action late in the first half as he got down low to save from Dario Lezcano.

After Yedlin was dismissed, Paraguay sensed a way back into the contest and surged forward in search of an equaliser.

But they were prevented from restoring parity by a combination of Guzan and excellent defensive work from his back four as the US hung on to clinch victory.

Costa Rica were determined to end their participation at the tournament on a positive and scored the fastest goal of the tournament through Johan Venegas’ long distance strike after just 87 seconds in their match with Colombia.

Colombia’s Frank Fabra then found the net at both ends, first equalising on the seven minute mark before he inadvertently turned Venegas’ cross into his own net.

Celso Borges extended the Costa Rican advantage just before the hour but Marlos Moreno pulled one back for Colombia, who weren’t able to find an equaliser as they dropped to second place in the group on goal difference.