Dempsey is now within one of Landon Donovan's all-time record for the States as he opened the scoring, linking up with Christian Pulisic only for Gabriel Gomez to equalise just before the break at the Estadio Rommel Fernandez Gutierrez. in Panama City.
The result leaves the USA with just one win from their four qualifiers as they sit one spot behind third-placed Panama.
Having hammered Honduras 6-0 in their last match, Bruce Arena made three changes with Jermaine Jones, Tim Ream and Graham Zusi all making the starting XI.
Panama were lively but they struggled to create clear-cut chances with Felipe Baloy coming close but was unable to keep a short-range header on target.
Pulisic threatened for the US with a last-ditch Luis Ovalle tackle denying him as chances started to flow with Tim Howard forced into a save by Alberto Quintero on the other end.
Somewhat against the run of play, the visitors went ahead through Dempsey in the 39th minute as Pulisic twisted down the right hand side playing through Dempsey to score from close.
However, Panama drew level in the 43rd minute after a long throw-in fell to Gomez in the area with the midfielder powering the ball past a helpless Howard.
Despite Panama continuing to push for a winner, USA held firm to leave with a point.