Frankie Bunn's side missed the chance to climb into the top half of the League Two table after Rovers fought back to secure a 1-1 draw.
In highly a competitive contest, a strike from Johan Branger gave the visitors the lead at the interval, but Rovers hit back through Jennings as they snatched a hard-earned point.
George Edmundson missed a header for Athletic early on, but there was little goalmouth action until six minutes before the break when Tranmere failed to clear a corner and Branger drilled home from 12 yards out.
Ishmael Miller had a chance to double Athletic's advantage after 67 minutes but, under pressure, he dragged his effort wide.
When substitute Sam Surridge went clean through on goal for Athletic he tried to go around Scott Davies, but the Rovers 'keeper got a hand to it - denying a certain second.
And Athletic paid a heavy price for their missed chances when 18 minutes from time, a hopeful ball into the box fell nicely for Jennings who fired home the equaliser.
Athletic are back in action on Tuesday (7.45pm) when they host Lincoln City.
