Angel Rangel opened the scoring when his shot came off ex-Bolton goalkeeper Jussi Jaaskelainen and into the net although the Swans' player was credited with the goal.
Michu and Danny Graham got the other goals as the Swans made light of the departure of former boss Brendan Rodgers.
Rangel was not looking too far ahead though and told Sky Sports 2: "It's good not to be conceding goals and good to be scoring them but it's early days."
Of his fortuitous goal, he added: "I'll take it.
"It counts - that is what is important.
"I think overall it was a good performance."
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Winger Nathan Dyer credited Michael Laudrup for their scoring prowess, saying: "He has brought his own ideas in.
"He has given us a more free role to get our shots off.
"We've got to work hard now, make sure we have performances like this week in week out."
Scott Sinclair did not make an appearance for Swansea and Laudrup revealed the pair had spoken yesterday with the winger not intending to sign a new contract.
Laudrup said: "Scott and I talked yesterday about a lot of things.
"The last two or three days lots of things have been going on around him.
"We will see what happens next week.
"If he leaves we will have to take it from there. I really don't know."
Of where the Swans find themselves after two games, Laudrup was clearly delighted.
"Two games, six points and two clean sheets - it's fantastic," he said.