The Republic need just a draw against Armenia in their final qualifer to secure a Euro 2012 play-off spot after this comfortable win over the minnows.
Robbie Keane hit the bar before Kevin Doyle hooked in a fourth minute opener.
The visitors moved 2-0 ahead when an Aiden McGeady shot was pushed out by Josep Gomez but the ball struck Marcio Vieira and flew into his own net.
The woodwork denied McGeady after the break while Stephen Ward is banned for the Armenia game after being booked.
It didn't take long to realise why Andorra lie at the bottom of the world rankings.
Doyle could have scored within a minute, with his shot well saved by the alert Gomes.
Keane was next to go close three minutes later and the striker fired against the bar after his initial shot was blocked.
A goal was coming and it arrived on seven minutes when Doyle hooked the ball past Gomes from John O'Shea's knock-down.
A clever free-kick led to the second goal in the 20th minute - Glenn Whelan slipped the ball to the unmarked McGeady and his fierce shot was parried out by Gomes, only to hit the unlucky Viera with the ball flying back into the net.
Keane blazed over before Ward picked up a costly yellow card for simulation.
The pace slowed in the final 15 minutes of the first half with the Republic safe in the knowledge that this Andorra team was not going to score two goals.
The second half fizzled out after an early burst from the Republic.
Keane was sent through by Doyle's flick-on but Gomez was quickly out to smother the shot.
McGeady nearly completed a double on 50 minutes with the Spartak Moscow winger's low drive hitting the outside of a post.
Darren O'Dea flicked the ball over from eight yards while O'Shea and substitute Shane Long were off-target with headed efforts late in the game.
Group leaders Russia are on course to take the automatic qualifying place after a 1-0 win in Slovakia, and with their final game at home against Andorra.
The Republic are two points back in second and a point ahead of Armenia, who beat Macedonia 4-1, so the winners at the Aviva Stadium are set to take the play-off position.
Andorra: Josep Anton Gomez, Bernaus, Gutierrez (Lorenzo 78), Emili Garcia, Lima (Sonejee 80), Christian Martinez, Pujol (Sebastian Gomez 59), Ayala, Vieira, Silva, Moreno.
Subs not used: Perianes Meca, Sanchez, Marc Garcia, Peppe.
Booked: Christian Martinez,Ayala.
Rep of Ireland: Given, St. Ledger, O'Shea, O'Dea, Ward, McGeady, Whelan (Fahey 65), Andrews, Duff (Hunt 75), Doyle (Long 71), Keane.
Subs not used: Forde, Kelly, Cox, Lawrence.
Goals: Doyle 7, McGeady 20.
Ref: Libor Kovarik (Czech Rep).