Swansea continued its excellent start to the Premier League season with a handsome 3-0 win over West Ham at the Liberty Stadium.
Swansea did not have Scott Sinclair in its squad, with the winger's move to Manchester City seemingly drawing nearer.
But in Dyer and Routledge they had the game's standout performers as the wide pair reveled in the freedom Laudrup has allowed them and toyed with a fragile Hammers back four.
Dyer credited Laudrup for the scoring prowess.
"He has brought his own ideas in," Dyer said on Sky Sports. "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."
The win moved Swansea top of the Premier League for a few hours, and Laudrup will be equally delighted by a second clean sheet.
"It is great for the supporters and they have to enjoy it," Laudrup said. "I said it the other day, it's a dream, but for us on the pitch we can't permit ourselves to dream, we have to live in reality, but let's enjoy today."
West Ham, with James Tomkins brought into midfield to track Michu, enjoyed a good start with their hosts uncharacteristically wasteful in possession.
That growing threat produced the opening goal in the 20th minute.
And for the second game in a row, after Rob Green's howler at Loftus Road last week, Swansea was gifted the lead by a goalkeeping error.
Patient build-up work involving Michu and Dyer played Rangel in on the right of the area, and Jussi Jaaskelainen could only help his low cross into the net.
"I'll take it," Rangel said on Sky Sports. "It counts -- that is what is important. I think overall it was a good performance."
The temperature went up a few notches as Michu's wild hack caught Tomkins, and the Spaniard was involved again as he exchanged heated words with Nolan after the midfielder's heavy challenge.
James Collins had also got involved in the spat but moments later he gifted Swansea a second goal.
"We have been punished severely for two very big errors by Jussi and James," West Ham manager Sam Allardyce said. "Mistakes by our two most experienced players, who have a huge amount of experience in this league, have cost us the game today."
The Wales defender's back-pass sold Jaaskelainen short and Michu pounced to slot low into the left corner.
Jarvis had cut a frustrated figure for the Hammers, and those feelings only increased when he was denied a debut goal by Vorm.
The winger's superb close-range volley from a Tomkins header was brilliantly beaten away by the Dutchman, while at the other end Neil Taylor narrowly failed to finish a flowing Swansea move as Nolan's block diverted his shot over the bar.
The hosts had on occasion been troubled by West Ham's direct approach and they were fortunate to get to the break with their advantage intact.
From a series of set-pieces Rangel blocked a Nolan effort, Vorm kept out a Tomkins header and Leon Britton was in the right place to clear Cole's header off the line.
With the Hammers needing a greater goal threat, Allardyce removed Tomkins from his containment role and put on Ricardo Vaz Te.
But it was Swansea that remained the brighter attacking spark and Jaaskelainen had to get down low to parry away a Danny Graham effort five minutes into the second half.
Graham should have made it three a few minutes later. Dyer jinked his way into space on halfway and fed the striker, but he put his effort wide of the far post.
However, the forward did bag his first goal of the season after 63 minutes, firing home after more delightful link play between Dyer and Routledge.
"We have small players in Wayne and Nathan who can turn fast with the ball," Laudrup said. "They are so fast turning with the ball and they create so many problems for defenders. They get in between the defensive lines and that makes them very dangerous."
Further chances were passed up as the Swans toyed with the visitors at times, but it did little to diminish the euphoria of the home support as their side went to the summit of the Premier League.
Information from Press Association was used in this report.