The hunt for a first Premier League goal and victory is over after the Swans brushed aside West Brom 3-0 at the Liberty Stadium.
Scott Sinclair became the first player to score a Premier League goal outside of England as he slotted home from the penalty spot after Joe Allen was taken down in the box by Paul Scharner.
Leroy Lita then headed home from close range before Nathan Dyer blasted home in the second half to finish off a hugely satisfying afternoon for Brendan Rodgers.
The only sour note of which was the head injury to Neil Taylor in the latter stages, as the Wales international was stretchered off and had stitches put in following a challenge by Peter Odemwingie.
Swansea City captain Garry Monk made his first Premier League appearance for the club as he replaced Steven Caulker at the back after the Tottenham Hotspur loanee picked up a knee injury in last week's defeat at Arsenal.
Also missing was striker Danny Graham, the club's record transfer signing, who was left out with a back problem after failing a fitness test. That meant Lita made his first league start for the Swans.
Mark Gower also got his first league start following on from his first top-flight appearance at the Emirates last time out. He came in for Kemy Agustien, who was sidelined with a hamstring injury.
Swans:Michel Vorm, Angel Rangel, Garry Monk (capt), Ashley Williams, Neil Taylor (Fede Bessone, 86), Leon Britton, Mark Gower, Joe Allen, Nathan Dyer (Wayne Routledge, 70), Scott Sinclair, Leroy Lita (Luke Moore, 70). Unused subs:Stephen Dobbie, Gerhard Tremmel, Jazz Richards, Lee Lucas.
West Brom: Ben Foster, Steven Reid, Nicky Shorey, Jonas Olsson (capt), Craig Dawson, Jerome Thomas (Chris Brunt, ht), James Morrison, Yosouff Mulumbu (Graham Dorrans, ht), Paul Scharner (Simon Cox, 63), Shane Long, Peter Odemwingie. Unused subs: Marton Fulop, Marc-Antoine Fortune, Billy Jones, Gareth McAuley.
Referee: Martin Atkinson
The Jack Army was in fine voice before kick-off as they looked to help the Swans get off to a positive start.
In a difficult week or so for both clubs, who had lost people closely linked with them, there was applause and a minute's silence to remember them.
The whole nation was in mourning following the tragic deaths of the four miners in Pontardawe - Phillip Hill, Charles Breslin, Garry Jenkins and David Powell - along with the death of five-year-old Harry Patterson and Brendan Rodgers's father Malachy.
West Brom, too, were still in mourning following the loss of a member of their squad - young Blake Melbourne.
The home crowd were looking for a positive start, and they got one.
Scott Sinclair turned an early strike just past the near post, before the Liberty was on its feet.
Sinclair found Joe Allen in the box and he outfoxed Paul Scharner, with the midfielder bringing down the Wales international in the box.
Referee Martin Atkinson pointed to the spot, and Sinclair was poised.
Cool as can be, the winger sent Ben Foster the wrong way with his effort finding the bottom right corner.
The Liberty was fully charged, and the threat of becoming the first side to not score in the opening five Premier League games were over.
West Brom could have been level after 22 minutes as Neil Taylor's mis-pass fell to Shane Long, but the Irish striker blasted high and wide from the edge of the box.
It was a great chance, and the Baggies would pay for that miss as just two minutes later the Swans doubled their lead.
Mark Gower's corner found the unmarked Sinclair on the penalty spot, and his glancing header reached Leroy Lita, who nodded home from six yards.
The striker - a £1.75m signing from Middlesbrough this summer - celebrated passionately, though he was booked for removing his shirt.
At the other end, Long drove a sweet 20-yard half-volley which Michel Vorm reacted well to tip over.
The Swans comfortably saw out the remainder of the half, controlling the tempo and possession well.
Half-time: Swans 2 West Brom 0
Roy Hodgson made two changes at the break with Chris Brunt and Graham Dorrans replacing Jerome Thomas and Yosouff Mulumbu.
The Baggies boss was looking for an instant reaction from his side as they looked to claw their way back into the contest.
But it was the Swans who flew out of the traps as goal number three arrived. Lita flicked on a clearance from Vorm, and Dyer raced on and shrugged off his marker before blasting inbetween Foster's legs and into the net.
Williams then made a perfectly-timed block on James Morrison before Vorm flew across his line to tip Dorrans' top-corner bound free-kick over the crossbar.
Brendan then made two changes, with former Baggies striker Luke Moore replacing Lita and Wayne Routledge coming on for Dyer.
Shortly after their introductions, the game was brought to a halt as Peter Odemwingie collided with Neil Taylor as the left-back was heading away a cross.
Medics were brought onto the pitch before he was stretchered off to a large applause.
Fede Bessone came on in his place as the Argentinian made his first appearance since returning to the club following a spell at Leeds.
Nine minutes of added-on time were signalled as the game ticked past the 90th minute, with West Brom pushing for a consolation.
They went close, Long rising high to nod Morrison's cross towards the bottom corner, but Vorm dived low to keep it out.
Then, after a flowing passing move, Joe Allen pushed on before teeing up Mark Gower, but his effort was deflected wide for a corner.
That was it for the action, as the Swans claimed their own piece of Premier League history.