The Legia striker had scored the stoppage time equaliser at the Pepsi Arena last week to deprive Pat’s of a memorable away win.
Last night he put the Poles in the driving seat with an opportunist opening goal before adding a third as Legia showed their class.
In between, Michal Zyro had already all but sealed Legia’s passage through to a third qualifying round meeting with Celtic with their second goal.
But there was more misery for St Pat’s late on as they conceded a fourth goal from substitute Marek Saganowksi while a Conan Byrne own goal completed Legia’s emphatic win and St Pat’s despair.
Celtic manager Ronny Deila and his assistant John Collins were very interested spectators in a near to its 6,000 capacity Dublin 24 venue.
And buoyed both by their display and result in Poland, St Pat’s were assertive from the start with Christy Fagan and Killian Brennan having shots blocked away within two minutes.
Brennan then got a shot on target, straight at Dusan Kuciak, two minutes later.
But there were nerves at the back as captain Ger O’Brien’s wayward pass under no pressure gifted Legia their first opportunity on 10 minutes.
The ball was straight to visiting skipper Ivica Vrdoljak who picked out Ondrej Duda to get away a low drive Brendan Clarke did well to hold onto.
A lapse in concentration then cost St Pat’s a goal on 25 minutes to put Legia ahead in the tie for the first time.
The Inchicore men switched off momentarily as they thought Greg Bolger had been fouled in midfield.
The punishment was clinical with Zyro putting Radovic in to shoot low to the corner of the net.
The St Pat’s response was positive and they were almost level seven minutes later from their most incisive move of the match.
Brennan slipped Keith Fahey in and his deflected shot was touched out for a corner by the rapid reaction of Kuciak.
Buckley brought on the experienced Mark Quigley for the anonymous Chris Forrester at half-time. But it was Legia who continued to show the better composure on the ball and create chances.
Vrdoljak and central midfield partner Romasz Jodlowiec carved St Pat’s open on 57 minutes for Michal Kucharczyk to bring a save out of Clarke.
A half chance fell St Pat’s way two minutes later; Fahey’s first time volley was just off target as Legia only half cleared Byrne’s corner.
Legia remained much the better side, though, and Lukasz Broz’s ball over the top caught St Pat’s square as they were relieved to see Radovic blast his volley directly at Clarke.
St Pat’s lost O’Brien to injury just past the hour and the game soon fully slipped away from them.
Tomasz Brzyski was narrowly wide with a free kick before Legia rubber-stamped their deserved victory on 69 minutes.
Kucharczyk did well to get to the end line to pull back for Zyro whose shot squirmed through Clarke to the corner of the net.
Duda then set up Radovic to add his second goal of the night on 82 minutes before Jakub Kosecki got to the end line to cross for fellow substitute Saganowski to score the fourth three minutes from time.
Byrne headed a cross from Bryzski into his own net in the first minute of added time to compound St Pat’s misery.
ST PATRICK’S ATHLETIC: Clarke; O’Brien (Hoare, 62), Foran, Browne (Lynch, 73), Bermingham; Fahey, Bolger; Byrne, Brennan, Forrester (Quigley, h/t); Fagan.
LEGIA WARSAW: Kuciak; Broz, Rzezniczak, Astiz, Brzyski; Zyro, Vrdoljak, Jodlowiec, Kucharczyk (Kosecki, 85); Duda (Saganowski, 85); Radovic (Piech, 87).
Referee: Andreas Ekberg (Sweden).