Mexico defeated Guyana 3-1 at home, with Group A favourites USA triumphing by the same scoreline against visiting Antigua & Barbuda.
Rangers defender Carlos Bocanegra opened the scoring for the USA only six minutes into the match, with Clint Dempsey doubling the advantage just before half-time with a penalty.
Peter Byers reduced the deficit after 64 minutes, but then Herculez Gomez restored the two-goal cushion with 18 minutes to go.
The result was satisfactory but head coach Jurgen Klinsmann is hoping for more as the campaign progresses.
"We created enough chances, but then you've got to be clinical enough to put them away", said Klinsmann.
"We know we have to step it up a lot going into the next match, which we surely will do."
In the other Group A match in Kingston, Jamaica had to work hard to defeat Guatemala 2-1.
Forward Demar Phillips (40) and Ryan Johnson (46) put the hosts in front, with Dwight Pezzarossi hit back for the visitors in stoppage time.
In Group B, Mexico claimed were workmanlike in their win over Guyana at Aztec Stadium.
Carlos Salcido sent the hosts ahead after 10 minutes and Giovani Dos Santos extended the lead with a long-range effort five minutes later.
Javier Hernandez and Andres Guardado combined to force an own-goal from John Rodrigues to make it 3-0 before Hector Moreno also diverted past his own keeper for a consolation.
Despite the victory, Mexico were booed by some fans who had expected a bigger margin.
Coach Jose Manuel de la Torre admitted: "We didn't play well, the people always have a reason. We have to improve a lot in the next games.
Hernandez added: "The most important target was the victory, and we obtained it. I don't care if we win 10-0 or 3-1, we always want to improve and this result give us space to work."
Elsewhere in Group B, El Salvador rescued a 2-2 draw in Costa Rica.
Alvaro Saborio (10) and Joel Campbell (15) gave the Ticos an early lead but Isidro Gutierrez pulled one back in the 23rd minute.
A power failure followed and when the match resumed Osael Romero was on hand with a 55th-minute strike.
In Group C, 10-man Canada defeated Cuba 1-0 in Havana.
Olivier Occean was the scorer, heading home 10 minutes into the second half.
The Canadians defended that lead even after goalkeeper Lars Hirschfeld was sent off in the 64th minute.
Meanwhile, Blas Perez hit two second-half goals to hand Panama a 2-0 away win over Honduras.