Home captain Bryan Ruiz restored the lead when he found the net shortly before halftime and neither side could add to the scoreline after the break as Costa Rica held on to take all three points.
The result enabled the 2014 World Cup quarter-finalists to move onto 11 points in the six-team Hexagonal group, three behind leaders Mexico but three ahead of the United States, who battled to a draw in Mexico City on Sunday.
Panama sit fourth on seven points, while Honduras are fifth on five points, and Trinidad and Tobago bottom on three.
In the other group game, Panama and Honduras cancelled each other out in an action-packed 2-2 draw in Panama City as the hosts wasted an opportunity to climb above the United States.
Romell Quioto put the visitors ahead after six minutes but Blas Perez replied with a header four minutes before the break.
Alberth Elis put Honduras back in front with a smart goal on the counter attack 20 minutes into the second half but Panama, who have never qualified for the World Cup, salvaged a draw when captain Roman Torres headed in a last-minute equaliser.
The top three teams in the group qualify automatically for Russia 2018, while the fourth-placed finisher can still advance through a playoff against a side from the Asian confederation.
(Reporting by Andrew Downie; Editing by John O'Brien)
