The Maltese champions moved into a shock lead on nine minutes as Brandon Paiber collected the ball on the edge of the box with his back to goal and touched a pass into the path of the advancing Matias Nicolas Garcia.
Garcia’s drive from distance took a slight deflection that proved decisive to steer the shot beyond Chris Johns between the Blues posts.
Linfield’s response featured a dangerous free-kick delivery by Niall Quinn from wide on the right which reached the far post but Jimmy Callacher’s hooked attempt dropped the wrong side of the upright.
Strong play again by Piaber signalled the threat of Floriana on the counter-attack but his shot cleared the crossbar.
Ethan Boyle posed a threat from the right flank but Linfield failed to add any cutting edge, with Floriana also close to converting a ball into the box but the low cross proved just beyond two sliding attackers.
Linfield increased the tempo as play progressed but had to wait until 44 minutes to offer any test to Floriana’s Ini Akpan, with Navid Nasseri’s shot from outside the area lacking the power to trouble the goalkeeper.
The second of back-to-back injury-time corner-kicks by Linfield offered Boyle an opportunity but his header dropped wide from a promising position.
The Irish League champions attacked from the first whistle of the second half as Northern Ireland international Shayne Lavery moved forward at pace and burst into the box but Akpan raced out to block the shot from the tight angle.
Clever play moments later by Lavery inside the danger area had Floriana on the backfoot, with the ball flashed goalwards by Stephen Fallon but Akpan’s reaction save pushed the effort out - with Bastien Hery hooking over the bar.
A double substitution past the hour mark led to the introduction of recent arrival Christy Manzinga and experienced striker Andy Waterworth off the substitutes’ bench.
Waterworth offered an instant example of his penalty-box prowess by hooking goalwards, with the deflection leading to a corner-kick which, once again, exposed Akpan’s lack of comfort in the air.
Another snapshot by Lavery from a tight angle had Akpan scrambling to save as the Blues increased the pressure in search of an equaliser.
However, the Blues suffered a blow on 73 minutes when Ross Larkin’s second bookable offence reduced Linfield to 10 men for the closing stages.
Larkin’s attempt to cut out the threat, after an error by Boyle steered the ball towards the danger zone, ultimately led to red for the centre-back.
Linfield’s late bid to rescue the tie featured a penalty appeal waved away by referee David Munro.
Akpan then produced a superb one-handed stop inside the packed penalty area in the final moments to claw away Jimmy Callacher’s close-range header off a delightful Quinn cross.
Manzinga’s acrobatic back-post effort lacked a clean connection and Floriana finished in front for a major moment in the Maltese club’s European history.
LINFIELD: Johns, Larkin, Callacher, Lavery, Nasseri (Waterworth, 62), Clarke (Manzinga, 62), Fallon, Hery (Kearns, 77), Mulgrew, Boyle, Quinn.
Subs (not used): Stafford, McClean, Pepper, Moore.
FLORIANA: Akpan, Dias, Ruíz, Venancio da Silva, Camenzuli, Leone, Keqi (Cheveresan, 83), Pisani, Fonseca, Paiber (Arias, 61; Beye, 86), Garcia.
Subs (not used): Cassar, Cini, Busuttil, Agius.
Referee: Munro (Scotland)