Regional heavyweights Mexico were minutes away from missing out on the fourth-placed playoff spot when they were beaten 2-1 in Costa Rica and Panama held a 2-1 lead over the Americans.
But Panama, who needed to win to leapfrog Mexico in the six-nation qualifying tournament, conceded two goals in stoppage time to lose 3-2.
Mexico now face Oceania winners New Zealand in a two-leg playoff in November in an effort to continue their long streak of World Cup appearances while Honduras will make their third appearance at the game's showpiece event.
Honduras made the perfect start against Jamaica when Carlo Costly scored in the first minute but the home side, who failed to win a match in the final round, drew level two minutes later through Je-Vaughn Watson.
Honduras regained the lead after 33 minutes to go into the break with a 2-1 advantage when Maynor Figeuroa scored off a free kick but Jamaica equalised in the second half when Rodolph Austin converted a penalty.
Honduras survived some anxious moments but their defence held firm before the players celebrated booking their passage to Brazil.
Mexico have qualified for every World Cup since 1982, with the exception of 1990 when they were banned by FIFA after fielding over-age players in a youth tournament, have the chance to qualify after an extraordinary final week.
Last Friday, they needed a stunning goal from Raul Jimenez five minutes from fulltime to beat Panama at home then on Tuesday needed the help of the U.S. to keep ahead of Panama.
Mexico fell behind early against Costa Rica when striker Brian Ruiz scored for the home team in the 26th minute.
Although Mexico equalised three minutes later through Oribe Peralta, whose shot hit the underside of the bar, Costa Rica went back in front when Alvaro Saborio headed what proved to be the matchwinner in the 64th minute.
Mexico's hopes of staying alive rested on the result of Panama's match with an understrength American side, who had the luxury of resting some of their regular starters after already finishing top of the group standings.
Panama, who have never qualified for the World Cup, led 1-0 at the break after Gabriel Torres found the back of the net in the 18th minute.
Michael Orozco brought the Americans back on level terms in the 64th minute but Panama regained control when Luis Tejada scored seven minutes before fulltime, tapping in a rebound.
The goal set off wild celebrations in the Rommel Fernandez Stadium but the cheers turned to disbelief when a header from Graham Zusi then a long range strike from Aron Johannsson in injury time ended their World Cup hopes.
(Reporting by Julian Linden in New York; editing by Greg Stutchbury)
