Worcestershire is currently at 137 for 2 with Roderick scoring an unbeaten 53, trailing behind Kent who scored 171 runs with Muyeye top-scoring with 56. Joe Leach was the standout performer for Worcestershire, taking an impressive 6 wickets for 52 runs. Worcestershire is now trailing by 34 runs.
Worcestershire all-rounder Joe Leach made a successful return to action after injury with a six-wicket haul on day one of the Vitality County Championship encounter with Kent at Visit Worcestershire New Road.
Leach finished with 6 for 52 from 11.5 overs - the second-best figures of his career - as Kent were dismissed for 171 in 49.5 overs after being put into bat.
It was his first appearance since the Championship match against Nottinghamshire in late May because of a recurrence of a knee problem and he is hanging up his spikes at the end of the campaign.
But Leach's determination to return for the finale of the season paid off handsomely once he had settled into his rhythm in his second spell from the New Road End after conceding 26 runs in his first four overs.
Three wickets in 13 balls undermined Kent's promising start and they subsided from 73 for 0 and lost 10 wickets for 98 in 32.4 overs.
There was also an encouraging debut for New Zealand paceman James Hartshorn who bowled a nagging line and length.
But the bowlers were also backed up by some fine catching behind the wicket, most notably by Rob Jones who held onto four chances at second slip.
Gareth Roderick continued his fine form with a half century to spearhead Worcestershire's reply and they closed 34 in arrears with eight wickets in hand.
Worcestershire handed an opportunity to Hartshorn after fellow Kiwi Nathan Smith was forced to cut short his spell at New Road through injury.
Captain Brett D'Oliveira, Kashif Ali, Leach and Adam Finch all returned after lengthy spells on the side-lines. Kent included new signings in pace duo Alfie Ogborne, on loan from Somerset, and West Indian Akeem Jordan.
D'Oliveira put Kent into bat and Tawanda Muyeye adopted an aggressive vein with a succession of boundaries. But he was fortunate to edge Hartshorn just short of second slip and twice flashed hard at Finch as the ball flew over the slip cordon.
He completed a 62-ball half-century with his 10th boundary but the game turned on its head after Leach switched to the New Road End. Muyeye (56) pushed forward to a delivery which left him and Jones held onto a fine catch away to his left at second slip.
Kent skipper Daniel Bell-Drummond was undone by a similar ball with Ethan Brookes at third slip making no mistake. Leach had settled into a perfect rhythm and Jack Leaning edged through to keeper Gareth Roderick.
Worcestershire continued to apply the pressure in the immediate post lunch session with three more quick wickets.
Finch, whose first two overs had cost 27 runs, returned and accounted for Joey Evison who drove hard at a ball which nipped away and was caught behind.
Hartshorn picked up his first wicket for the county as Harry Finch cut a delivery which swung away to Jake Libby at backward point.
It became 103 for 6 when Finch found the inside-edge of Ben Compton's bat and Roderick did the rest for his third catch.
At that point Kent had lost six wickets for 30 runs in the space of 15.4 overs.
There was a deserved first breakthrough for Taylor when Matt Parkinson flashed hard and Jones made no mistake at second slip.
Leach collected a fourth scalp when Grant Stewart went for a big hit back down the ground and had his off stump knocked back.
He polished off the innings in quickfire fashion with Jones holding onto two more sharp opportunities at second slip to dispose of Alfie Ogborne and George Garrett.
Roderick and Libby then provided Worcestershire with an assured start to their innings and the 50 came up in only 11.1 overs.
The partnership was worth 89 when Libby (30) pushed forward to Ogborne and was caught behind.
New batter Kashif Ali quickly brought up the Worcestershire hundred with a cover drive for four off the same bowler but on 17 he fended a delivery of extra bounce from Jordan to first slip.
Roderick completed a 107-ball half-century with seven fours.