Michael Laudrup’s Capital One Cup winners all but killed off the third qualifying round tie with a convincing success at the Liberty Stadium.
Bony headed in Wayne Routledge’s neat cross and then scored his second after strike partner and fellow goalscorer Michu saw a shot come back off a post.
“I feel good, but the most important thing was to win this game and not concede a goal,” Bony said.
“It’s very good for us, we can enjoy tonight and think about the next game.”
Alejandro Pozuelo completed the scoring but it was the partnership between Michu, last season’s bargain signing, and £12 million Bony which will have most excited fans in south Wales.
And Bony added: “It’s going well, I am trying try to get to know Michu more and more because it is just my second game. It’s important to concentrate in every training (session) and every game.”
Coach Michael Laudrup added: “They need games, of course. At Reading they played a bit together so it’s only the second game.
“We had five new players, we need some time for everyone to get to know each other but if we win 4-0 in a game like this with a lot of people not knowing each other yet... not bad, huh?
“It’s a perfect night. Four goals, not conceding any away goals, two goals from the new man Bony, Michu is back scoring a goal, Pozuelo got a goal in his first game for the club, no injuries — it’s perfect.”
SWANSEA: Vorm, Rangel, Williams, Amat, Davies, Dyer (Pozuelo 73), Britton (Canas 80), Shelvey, Routledge, Michu (de Guzman 66), Bony.
MALMO FF: Dahlin, Albornoz, Jansson, Helander, Ricardinho, Hamad (Kroon 82), Halsti, Thern, Friberg (Forsberg 67), Rantie, Eriksson (Johansson 76).
Referee: Paolo Mazzoleni (Italy).
Selected Europa League results: FC Minsk 0 St Johnstone 1, Motherwell 0 Kuban Krasnodar 2.