Clark scored the opener ten minutes before the interval against the run of play after Poland could only partially clear James McClean's corner.
Earlier Robert Lewandowski had a great opportunity to put the visitors ahead when played in one-on-one with David Forde but the Ireland keeper got down well to block with his legs and clear the danger.
Hoolahan then made sure of the win with an accomplished finish on 76 minutes after fellow substitute Jeff Hendrick had picked him out in the box.
The scoreline in Dublin perhaps flattered Giovanni Trapattoni's men, who were decidedly second best before the break.
However, goalkeeper Forde responded to the challenge of being brought into the starting line-up with a series of important saves to keep them in it.
Then soon after the restart, James McCarthy sent a side-footed effort towards goal, only for substitute keeper Wojciech Szczesny to make a fine fingertip save.
As the game wore on, the hosts grew in confidence and finished strongly to remind their fans of the heady days before a disastrous Euro 2012 campaign when they were difficult to beat.
They might have extended their lead with 62 minutes gone when defender Damien Perquis sliced McClean's cross straight to Conor Sammon. He homed in on goal, but took a heavy touch as he prepared to shoot and Szczesny pounced to intercept.
But Hoolahan made no mistake 14 minutes from time after controlling the ball on his chest before volleying past the helpless Szczesny to seal the win.
While Trapattoni will restore his tried and tested players to the starting line-up for next month's crucial World Cup qualifiers against Sweden and Austria, he will do so confident that his options appear to have increased.