Byrne and Lynch's goals cancelled out the earlier strike by Conor O'Grady, who had given the Sligo side early hope of overhauling the 4-1 defeat they suffered in Richmond Park on Tuesday night.
O'Grady gave the tie a much needed jolt in the 10th minute when, after a typically long Richard Brush kick-out, Matthew Blinkhorn headed the ball into the midfielders path. He let the ball bounce and half-volleyed home from 25 yards, low and hard in a perfectly executed finish.
Sligo nearly pulled the tie back to within one goal on aggregate soon after, as Dan Connor denied a header from Eoin Doyle at point blank range in the 23rd minute with an utterly fantastic save. From there on, though, it was all downhill for Sligo, as four minutes later St. Pat's levelled matters on the night and effectively put the tie to bed.
The ball was sent down the left wing to Vinny Faherty who duly crossed to the back post where it was sent back across by David McAllister. Paul Byrne stretched his leg as high as he could and just tipped the ball over Brush and the ball bounced over the line to effectively kill off Sligo's hopes of obtaining their first trophy since 2005.
Gary McCabe and Richie Ryan had efforts in the remaining minutes of the first half, but realistically they were nowhere near goal and with a three-goal deficit to potentially overturn, nowhere near good enough.
St. Pat's controlled the remainder of the game, whether they were in possession or not. Faherty had a shot on goal from 20 yards in the 47th minute and indeed had another chance in the 55th minute when Ryan Guy beat Paul Whelan on the left and crossed to the former Galway striker who shot wide.
The visitors then sent the Sligo fans into despair just minutes later when Damian Lynch put Pete Mahon's side 2-1 up. He marauded in from the left and chipped the ball into the box, where Brush seemed to trip over a stray body part and the ball trickled past the helpless 'keeper into the net.
Sligo had most of the ball for the remainder, but were quite lacklustre to say the least. Whelan shot over from the right on 68, and was denied by the woodwork with 11 minutes remaining.
The move was begun by Ryan, who fed the ball to John Dillon who got in behind the Pat's defence. In a one-on-one with Connor, Dillon chipped the ball across the goal to Dean Marshall who shot from close range, but his effort was stopped on the line by a St. Pat's defender, but only as far as Whelan, who smashed the ball off the post and wide in what was Sligo's last chance to at least salvage a draw from this contest ahead of their televised league encounter next weekend.
Sligo Rovers: Brush; Davoren (Whelan 50), Keane, Peers, Ventre; Doyle (Dillon 62), O'Grady, Ryan, McCabe (Marshall 62); Amond, Blinkhorn.
Subs not Used: Kelly, Foran, Feeney, Doninger.
St.Patrick's Athletic: Connor; Kenna, Guthrie, Lynch, Pender; Guy, McAllister, S Byrne (Coughlan 80), Mulcahy; P Byrne (Williams 63), Faherty (Sinnott 78).
Subs not Used: Rogers, Haverty, Harney, Doyle
Extratime.ie Man of the Match: Damian Lynch.