Northern Ireland moved top of their World Cup qualifying group after this impressive win at a sunny Windsor Park.
Warren Feeney finished from close range after 10 minutes but Poland levelled when Maik Taylor failed to keep out Ireneusz Jelen's shot.
Jonny Evans slid in to restore the lead and Northern Ireland went further ahead when Michal Zewlakow's backpass bobbled past keeper Artur Boruc.
Marek Saganowski pulled one back with a header but Northern Ireland held on.
The result took Nigel Worthington's side a point clear in Group Three after Slovenia and the Czech Republic, who started the day level with Northern Ireland on seven points, played out a scoreless draw.
Northern Ireland will now look to further improve their position when they take on Slovenia on Wednesday.
They made a positive start to the game when a superb Chris Brunt pass sent Feeney clear after three minutes but the Dundee United striker fired just wide.
An under-hit back-pass from Michal Zewlakow let in Healy five minutes later but the usually deadly marksman struck a weak shot which was kept out by Celtic keeper Boruc before the ball was scrambled away.
NI striker Warren Feeney dedicates his goal to his mother as she recovers from a broken leg
The deserved breakthrough came, however, when Boruc failed to collect Brunt's high cross to the back-post and Damien Johnston headed back to give Feeney the simple task of tapping in from four yards.
Poland levelled with their first meaningful attack as Jelen beat the offside trap, raced clear and produced a shot of such power that Taylor could only slow the ball down on its way into the net.
Play was stopped for over two minutes after an assistant referee was struck on the head by a coin, thrown from a section containing Northern Ireland fans.
When the action resumed, the tireless Feeney twice fired wide before the break as the home side failed to make their dominance count.
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