Jozy who? Eight days after controversially dropping the in-form AZ Alkmaar striker Jozy Altidore from the USA squad, Jurgen Klinsmann watched his team rout Guatemala to finally secure their place in the fourth and final round of Concacaf World Cup qualifying. A 3-1 win represented just the fifth time in 20 games under Klinsmann that they had scored more than one goal. The fourth had arrived last Friday, again without Altidore, in Antigua.

In truth, though, these games were to serve not as a referendum on Altidore – who had seemingly irked the manager with his attitude during a training camp earlier this year – but on Klinsmann himself. Appointed last year by US Soccer, the German had thus far failed to convince a nation's supporters that he was worthy of a $2.5m per year base salary, roughly four-times the sum received by his predecessor Bob Bradley.

Entering into these final two fixtures of the third qualifying stage, Klinsmann's team were far from assured of their progress. Level with Jamaica and Guatemala in Group A with seven points from four games, they would require at least four more to be certain of going through. On a wet and windy night at Antigua's Sir Viv Richards Stadium last Friday, they had snatched victory only courtesy of a 90th-minute Eddie Johnson header.

If that result meant the USA would need only a point from their home game against Guatemala, then that would not have been enough to satisfy a public who have come to expect more. This country had not failed to qualify for a World Cup since 1986 and had not lost any of their last 18 meetings with Guatemala. Scraping by was no longer acceptable. The fans wanted evidence that this team was not regressing under its well-remunerated manager.

They had, after all, come prepared to do their part. Kansas City's Livestrong Sporting Park may not be the largest venue in the country but has become renowned nevertheless over recent years as the home to some of the most committed and boisterous support in Major League Soccer. The metal bleachers in the Members' Stand might have been home this time to the American Outlaws supporters club rather than the Kansas City Cauldron, but their volume was just as deafening.

"Just 16,000 people, I couldn't believe it," said the USA goalkeeper Tim Howard afterwards. In truth the figure had been nearer 17,000 – and would have been significantly higher were it not for Fifa restrictions which prevented the USA from filling the standing room areas that make up part of the stadium's usual capacity. "If you would have told me it was 40,000 I would still have told you that was a fantastic [noise]."

It was a noise that barely diminished even after a disastrous opening to the game. Moments after being denied a free-kick on the edge of the Guatemala area when Hercules Gomez's header deflected off the arm of a defender, the home side found themselves a goal behind. With nothing more sophisticated than a long ball downfield for Carlos Ruiz to chase, Guatemala had unpicked the home defense.

That the striker should find himself with so much room to run into was flabbergasting. On a team set up to defend first-and-foremost, he was the one clear threat – Guatemala's all-time leading scorer and the author of four goals in five games already in this qualifying round. He calmly rounded Howard before slotting home.

Carlos Bocanegra, at fault on Antigua and Barbuda's goal four days previously, had since been restored from left-back to his natural home in the centre of defense but was once again the key culprit – losing track of his man. Thankfully, he did not have to wait long to make amends. Five minutes later Clint Dempsey diverted a corner into his Bocanegra's path and the defender gleefully seized his opportunity.

While his team-mates celebrated, Clint Dempsey quietly went to retrieve the ball and began running back towards the centre-circle. The Guatemala defence had already been sent into a panic by one Johnson cross in-between the two goals and now the striker smelt blood. Eight minutes later, he would give his team the lead, sliding in to convert the same player's low cross.

It was Dempsey again who added the third, though perhaps even more credit was due to Michael Bradley, whose chip over the Guatemalan goalkeeper Ricardo Jerez Jr was weighted to perfection. The midfielder has been a key figure in both of the team's last two wins, his return to the team following injury providing Klinsmann's side with a vision and technical ability that few others in the squad can match.

At last there were flashes of the fluid, attacking football that Klinsmann had promised to bring to this team. At different times Graham Zusi and Johnson switched wings, then the latter took turns with Dempsey in a more central, advanced role. Such interchange unsettled the Guatemala defence, drawing them out of position. With better finishing from Johnson on two second-half chances they might have scored more.

That said, they might also have conceded more too – Tim Howard called into action most notably when pawing away a Jose Manuel Contreras shot across goal with the score still at 2-1, then hooking the ball away from Jonathan Lopez with his feet after spilling a shot midway through the second half. If this was a result that Klinsmann and his team could feel good about, then there is still much to be done.

Asked point blank what he felt he had learnt so far in his 15-month tenure, Klinsmann spoke only in broad terms about players improving, with a nod to the challenge of playing games in Central America and the Caribbean. "But I know about World Cup qualifying, it always goes down to the wire," he said – noting how Germany had only squeaked into the 1990 World Cup before going on to win it.

There is more to take away than that, as Klinsmann will surely reflect in the coming days as he reviews his team's performance in this game and throughout qualifying. He has, after all, pulled off at least one coup in the last few days with the recall of Johnson – who had not played for the national team since 2010 and prior to Friday not scored for them since 2008.

For some players, though, the biggest takeaway might have been the simple difference that a vocal support can make. "It was phenomenal," said Bradley. "I can't stress enough how big a difference that makes. When we step on the field and we feel like we're playing in front of a crowd that is 98% American and is going to push you and support you through 90 minutes no matter what – as a player and a team we appreciate that."

Not by chance has this team now gone its last 22 home qualifiers without a defeat.

As it happened