The last-gasp draw means that Costa Rica, who reached the quarter-finals in 2014, join Mexico as the second representative from the North, Central American and Caribbean region (CONCACAF).
The top three teams qualify automatically for Russia with the fourth-placed side going into a playoff with a team from the Asian confederation.
A lethargic Costa Rica looked as if they were playing for a draw from the outset of a match held over from Friday due to torrential rain in the capital city.
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Honduras, however, took the lead after 66 minutes when Eddie Hernandez powered home a header from nine yards out.
The home side were on the verge of missing out on the point they needed but grabbed the equaliser in the dying seconds when Waston headed home a cross from Bryan Ruiz.
In the remaining fixtures of the round, Honduras host Mexico on Tuesday, while Costa Rica go to Panama and the United States travel to bottom side Trinidad and Tobago.
The United States have 12 points and are favourites to take the third automatic spot but Panama and Honduras, both on 10, are still in with a chance.
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