Shaun Maloney hit the only goal as Gordon Strachan's side grabbed a crucial 1-0 Group D qualifying victory at Celtic Park.
That result means Martin O'Neill's men will be licking their wounds for the visit of America - who were also defeated on Friday - to the Aviva Stadium.
The US succumbed 2-1 to Colombia at Craven Cottage despite securing a 10th-minute lead when Jozy Altidore converted from the penalty spot.
Carlos Bacca and Teofilo Gutierrez grabbed the goals to seal success for the South Americans.
Klinsmann is certain to shuffle his pack, having sent DaMarcus Beasley, Jermaine Jones, Lee Nguyen and DeAndre Yedlin back to their clubs.
Jones, Nguyen and Yedlin are headed stateside for their respective MLS teams' post-season campaigns, while Beasley has been released due to the glut of left-back options at Klinsmann's disposal.
O'Neill, meanwhile, has opted to allow the Republic's record goalscorer Robbie Keane to return to LA Galaxy, after the striker's surprise axing against Scotland.
The boss will be desperate for his side, who were unbeaten in their previous four matches, to get back to winning ways.
That was certainly the rallying cry from Everton defender Seamus Coleman, who said: "We have to regroup now. We came here wanting to win the game but we would have been happy if we had left with a point in the end.
"But unfortunately we switched off for the corner and they scored. It is a horrible feeling. I know we pushed them back towards the end but it was not good enough and we’re all disappointed."
Ireland and the United States have met on eight previous occasions, with the latter coming out on top in two, losing four and earning a share of the spoils twice.
They last tackled one another in 2002, the Republic of Ireland winning 2-1 thanks to Gary Doherty's late winner.
