A goal from Gabriel Sara's was not enough to take points from the Swans in the Canaries' trip to Wales in a 2-1 loss in the Sky Bet Championship on Wednesday night.
The Swans took the lead inside three minutes through Jamal Lowe that initiated a response from Sara with the equaliser before the break.
Ten minutes from time saw the winner for the hosts after Adam Idah had the best chance to put Norwich ahead earlier in the second half.
David Wagner made three changes to his starting 11 in the midweek fixture, bringing in Tony Springett, Adam Forshaw and Hwang Ui-Jo from the bench against Birmingham City.
It was a bad start for the Canaries after a mistake at the back inside five minutes saw Norwich lose possession in a dangerous position and Matt Grimes was able to slot Lowe through on goal to put the hosts ahead.
Jamie Paterson worried Norwich further with a powerful shot on the edge of the box a few minutes later that was placed just high of the cross bar.
The Canaries' best move early on came from Sara and Jack Stacey, but the Brazilian was unable to place a pass into the feet of the latter, who was heading goalwards inside the box.
A free-kick on the left hand side level with the Norwich penalty area was met by an Angus Gunn punch cleared to safety at the 20 minute mark.
Norwich were able to lift the spirits of the travelling fans shortly after, when Jonathan Rowe burst down the left and his cross into the box wasn't cleared by any Swansea shirts and Giannoulis was able to find Sara's head for the equaliser.
The next attack saw Springett release Stacey from the half-way line for the perfect opportunity to shoot from the edge of the box, but his effort was tipped away by Carl Rushworth.
Paterson would test Gunn from distance later in the half and Jerry Yates flicked a chance towards the bottom left corner but with no joy.
Norwich came out at the break full of energy as Forshaw looped a perfect ball for Rowe on the wing, whose cross was unable to meet Springett rushing into the box.
Shouts for a penalty following a foul on Kenny McLean were waved away with 25 minutes to go.
A low shot from substitute Onel Hernández came from Stacey's brilliant track-back, who ran the length of the pitch to cross to the Cuban on the edge of the box.
Yates found the back of the net after a brilliant save from Oli Cooper's shot but the flag was raised for offside and no goal was given.
Idah was unfortunate to not take the lead for Norwich shortly after as a cross from Płacheta came in too fast to control and his header was fired high over the bar.
Shane Duffy was at the rescue for the Canaries as he managed to clear a shot from close-range off the line, but just minutes later the Swans found themselves in front again through Bashir Humphreys to make it 2-1, ten minutes from time.
Swansea: Rushworth, Key, Cabango (Tymon 64), Darling, Humphreys, Grimes, Patino, Cullen (Cooper 72) Paterson, Lowe, Yates (Kukharevych 90)
Unused subs: Fisher, Fulton, Naughton, Walsh, Ashby, Congreve
Goals: Lowe (3), Humphreys (83)
Bookings: Lowe (48), Key (52), Cullen (55), Cooper (76)
Norwich City: Gunn, Stacey, Duffy, Gibson, Giannoulis, McLean, Forshaw (Płacheta 58), Sara, Springett (Hernández 58), Rowe (Fassnacht 78), Hwang (Idah 58)
Unused subs: Long, Batth, McCallum, Fisher, Gibbs
Goals: Sara (22)
Bookings: Gibson (18), Rowe (61)
HT: 1-1
FT: 2-1
Referee: Tom Neild
Venue: Swansea.com Stadium
Attendance: 14,512