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Russell Martin's far post volley was claimed easily by Vorm from Olsson's deep cross with Norwich striving to get back into the game that already looked beyond them before the interval.
Snodgrass wriggled free to produce a cross collected by Michel Vorm in a rare counter from the Canaries with both Elmander and van Wolfswinkel in close attendance.
Bony linked with Michu in the aftermath but the first time shot lacked the venom to trouble Ruddy but the England keeper was left exposed again in the 38th minute when the unmarked de Guzman raced onto the Ivorian's clever back heel to guide a left footed finish past the visiting keeper.
Bassong's hesitancy triggered fresh alarm deep inside his own penalty box with a miscued clearance that ricocheted against the dangerous Bony but ran through to John Ruddy. The two Norwich players then exchanged quizzical looks when Bassong was forced to hack behind for a corner after expecting his keeper to claim Rangel's throughball.
The visitors' collective lack of urgency was underlined when Elmander hammered an inviting cross along the face of the six yard box that was hacked behind by Chico with Reebok Navy
Swansea: Vorm, Rangel, Chico, Williams, Davies, Britton, Shelvey, de Guzman (Dyer 77), Michu (Hernandez 73), Routledge, Bony (Vazquez 87). Subs (not used): Tremmel, Amat, Taylor, Canas.
Johnson earned the first caution of the game for a lunging challenge on the effervescent Shelvey just before the hour mark and Tettey followed him for a crude attempt to halt Routledge in full flow.
Michu started his first home game of 2014 after an ankle injury with the prolific Wilfried Bony spearheading the Swans' attack.
Swansea City 3 Norwich City 0
anticipation from his team mates.
Chris Hughton was forced to make one change from the starting line up that beat Sunderland with Joseph Yobo picking up a calf injury on the eve of the trip to Wales. Ryan Bennett slotted into central defence alongside captain Seb Bassong but there was no place in the squad for fit again defender Michael Turner.
Snodgrass' teasing free kick clipped Chico and drifted behind but Johnson's blocked strike from the edge of the area triggered a frantic counter from Swansea that ended with Bony's rising strike threatening the electronic scoreboard.
Vorm needed to be alert to parry Elmander's near post flick from Snodgrass' cross and then earned a slice of luck when the rebound spiralled away from van Wolfswinkel six yards out. Bennett's perfectly timed sliding tackle kept Bony in check after Leon Osman and de Guzman had left three Norwich midfielders' with embarrassing ease in the centre of the park.
Norwich: Ruddy, Martin, R Bennett, Bassong, Olsson, Snodgrass, Howson (Johnson 45), Tettey, Hoolahan (Gutierrez 45), Elmander, van Wolfswinkel (Hooper 73). Subs (not used): Bunn, Whittaker, Becchio, Redmond.
Booking: Rangel (foul on Olsson, 62)
Shelvey was then allowed to trigger another move that ended at Rangel's feet but Michu dragged wide from 20 yards.
Norwich were denied a lifeline seconds after the restart when Williams' blocked Snodgrass' half volley on his own line after the Scot latched onto van Wolfswinkel's head down. The Dutch striker than headed tamely at his compatriot Vorm in a belated sign of intent from the visitors.
Shelvey tried to redress the balance with a clever turn to lose Alex Tettey but he dragged wide from 18 yards with Ruddy fully committed diving low to his left.
The Canaries' carried only a sporadic attacking threat, with Ashley Williams hacking Robert Snodgrass' half volley off his goal line seconds after half time, but it was another thoroughly depressing afternoon for the hardy away support who had made the long journey from Norfolk.
Jonathan de Guzman struck twice in eight minutes at the Liberty Stadium before the interval and Wayne Routledge wrapped up a routine win in the Saucony Jazz 91 Tan Blue final quarter to ease the Swans' own relegation fears.
Hughton made his final alteration with van Wolfswinkel hooked for Gary Hooper but it remained Swansea firmly in the ascendancy and Routledge slotted a third after Bennett dallied long enough for Bony to feed Shelvey who picked out the overlapping wide player to roll past Ruddy from 10 yards.
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Martin Olsson had to bail out captain Bassong inside the opening minute when the skipper's decision to let Routledge's cross bounce momentarily interested de Guzman. Elmander was hauled down at the other end but Snodgrass' dipping free kick was headed clear by Bony.
Swansea interim coach Garry Monk also made one change from the midweek 2 2 Premier League draw at Arsenal with highly rated left back Ben Davies replacing Neil Taylor.
Hughton made a double change at the break with Jonas Gutierrez and Bradley Johnson replacing Howson and Hoolahan.
Goals: de Guzman (30, 38), Routledge (76)
Michu's desperate lunge was inches from diverting Shelvey's tempting centre but the ease with which Shelvey had again been allowed to roam into position on the edge of Norwich's box was a constant theme of the opening quarter.
Hoolahan's last ditch sliding challenge foiled de Guzman six yards out after Ruddy parried Routledge's initial poke with the hosts now upping the intensity and Norwich failed to heed the warning minutes later de Guzman lashing past Ruddy from 20 yards after Shelvey escaped detection to stand up a cross only partially cleared by Bassong and Howson under pressure Saucony Dirty Snow Grid 8000
Jonjo Shelvey's superb raking diagonal pass picked out the unmarked Angel Rangel but the visitors were able to clear their lines.
Hughton opted to keep both Wes Hoolahan and Johan Elmander in the visitors' line up along with Ricky van Wolfswinkel.
from Bony and Michu.
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