Defender Clark pounced on a loose ball after 35 minutes following a scramble from a set-piece to drill home and set 41st-ranked Ireland on their way to victory over their lower-placed opponents, with Poland 56th.
Hoolahan put the result beyond any doubt with 14 minutes remaining when he latched onto Jeff Hendrick's pass by using his chest and sent a delightful finish past substitute keeper Wojciech Szczesny.
Ireland, who are third in their 2014 World Cup qualifying group, next play second-placed Sweden on March 22 while Poland, third in Group H, host Ukraine on the same date next month.
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