Aston Villa defender Clark thumped home a 35th-minute shot to give Ireland the lead against the run of play, before Norwich midfielder Hoolahan - who had received warm applause when he was introduced as a second-half replacement for Shane Long - cemented victory 14 minutes from time with an accomplished finish.
The scoreline perhaps flattered Giovanni Trapattoni's men, who were decidedly second-best before the break.
However, goalkeeper David Forde responded to the challenge of being brought into the starting line-up with a series of important saves to keep them in it. And, 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.
The Italian will restore his tried and tested players to the starting line-up for next month's crucial World Cup qualifiers against Sweden and Austria, but will do so confident that his options appear to have increased.
Ireland's Polish community turned out in force, mirroring the green invasion of their country during last summer's finals when the Irish fans were so well received.
For much of the opening 45 minutes, the Poles would have been delighted with what they saw as their side dominated possession and created a series of opportunities to take the lead.
However, it was Ireland who went in ahead at the break after Clark's strike gave then an advantage they scarcely deserved.
The game had been billed as an opportunity for Trapattoni to take a look at some of his newer players - John O'Shea and Glenn Whelan were the only members of the initial XI to have started a game at last summer's finals - and accordingly, striker Conor Sammon was handed a senior debut while young wingers Robbie Brady and James McClean were given chances.
However, it was 33-year-old goalkeeper Forde, preferred to Keiren Westwood because he is playing regular first team football for his club Millwall, who had the chance to shine during the first half.
Poland were simply too slick for Ireland in the middle of the field as Jakub Blaszczykowski and Daniel Lukasic provided the ammunition for Borussia Dortmund striker Robert Lewandowski to threaten repeatedly.
Forde survived an early scare when he scuffed a clearance straight to Ludovic Obraniak and looked on gratefully as full-back Paul McShane deflected the ensuing shot wide.
But from then on, he turned in an assured display as Lewandowski set about the task of trying to give his side the lead.
He perhaps should have done just that with 29 minutes gone when he was played in behind the home defence and ran in on goal. But Forde stood tall and when Lewandowski finally pulled the trigger, the keeper blocked with his legs.
The hosts took a shock lead after Clark climbed well to meet a left-wing corner. Although keeper Artur Boruc palmed away his initial effort, the ball fell to the defender once again in the midst of a goalmouth melee and he drilled a low shot into the bottom corner.
Lewandowski tested Forde with a scuffed volley three minutes later, but it was the men in green who headed for the dressing rooms at half-time with something to defend.
They mind have had even more to smile about within three minutes of the restart when James McCarthy send a side-footed effort towards goal, only for substitute keeper Wojciech Szczesny to make a fine fingertip save.
For all the Poles continued to enjoy the better of the game, Trapattoni's men were making more of a fist of it as they tried to hit the visitors on the counter.
They might have extended their lead with 62 minutes gone when defender Damien Perquis sliced McClean's cross straight to Sammon. He homed in on goal, but took a heavy touch as he prepared to shoot and Szczesny pounced to intercept.
Poland could have dragged themselves back into the game two minutes later when Arkadiusz Milik worked his way into a promising position inside the Ireland penalty area. However, the substitute tried too many dummies as he tried to tee himself up and slipped and fell over.
The miss proved costly with 14 minutes remaining when substitute Jeff Hendrick crossed for Hoolahan, who controlled the ball on his chest before volleying past the helpless Szczesny.