The Blues', already trailing 2-1 on aggregate, were dealt a bitter blow early on when Bohemians' Paddy Madden struck in the fifth minute to put his side 1-0 ahead, giving Linfield it all to do.
David Jeffrey's side, winners of the inaugural Setanta Cup in 2005, were targeting their third appearance in a Setanta final, but their aim to overturn the deficit from the first leg was made that much harder thanks to Boh's early strike.
Weary legs could have contributed to the defeat, with the clash coming barely 48 hours after a gruelling Irish Cup semi-final victory over Coleraine.
Jeffrey made two changes to the side that defeated the Bannsiders at the weekend – Michael Carvill started in place of Philip Lowry and Aaron Burns replaced JP Gallagher.
Any hopes of a rousing comeback in this tie were dashed with Bohemians' opener on five minutes - striker Madden catching the home defence napping to rush onto Paul Keegan's long ball before slotting past Blayney.
The Blues should have drawn level five minutes later when Mark Rossiter's attempted clearance from his own box fell to Paul Munster, but with the goal at his mercy the striker rushed his shot straight at Barry Murphy.
Blayney was called into action on 21 minutes, clawing away a powerful header from Raffaele Cretaro after another pin-point cross from Jason Byrne.
Linfield enjoyed plenty of possession in the opening half but failed to threaten visiting keeper Murphy, as their Setanta aspirations appeared to be heading for the exit door.
The Blues almost drew level five minutes after the restart when Michael Gault's header was cleared off the line via the crossbar by Madden, and then Robert Garrett's deflected shot forced a diving save from Murphy one minute later.
If Linfield fans needed any more proof this wasn't going to be their night then Munster's glaring miss on 57 minutes was confirmation.
The striker ghosted onto Thompson's deft lay-off but could only prod wide from six yards out as Murphy rushed off his line.
Munster went close again on 66 minutes when he swivelled and shot just wide of the target.
Blues defender William Murphy then unleashed a venomous left foot volley that fizzed past Murphy's right hand post on 75 minutes.
Jeffrey introduced defender Noel Bailie with five minutes remaining, for his 999th appearance for the club and just one away from a golden milestone.
The veteran will be hoping to make his 1000th appearance on Saturday when Linfield could clinch the Carling Premiership title against Crusaders at Seaview.