Michael Laudrup's side showcased the swagger exhibited in the crushing win over QPR as strikes from Angel Rangel, Michu and Danny Graham sealed victory.
Carlton Cole had West Ham's best chance but saw his header cleared off the line while debutant Matt Jarvis had his volley saved by Michel Vorm.
Swansea did not have Scott Sinclair in their 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 revelled in the freedom Laudrup has allowed them and toyed with a fragile Hammers back four.
The win moves Swansea top of the Premier League, at least for a few hours, and the Dane will be equally delighted by a second clean sheet.
West Ham, with James Tomkins brought into midfield to track Michu, enjoyed a good start with their hosts uncharacteristically wasteful in possession.
Skipper Kevin Nolan just failed to get his head on a George McCartney cross, but Swansea slowly began to settle and looked threatening as Dyer, Routledge and Michu linked confidently.
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, they were 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.
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 was to gift Swansea a second goal.
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 Sam Allardyce removed Tomkins from his containment role and put on Ricardo Vaz Te.
But it was Swansea who remained the brighter attacking spark and Jaaskelainen had to get down low to parry away a Danny Graham effort five minutes into the second stanza.
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.
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.