The young back sliced through the Scarlets defence to open the scoring after a perfectly timed pass from Jonny Arr and grabbed a second amid confusion in the visiting ranks.
Wing Ben Howard capped a fine team length of the field move for a stunning third home score.
The Welsh region replied with a try from Nick Reynolds but the win was no more than Warriors deserved for another display full of attacking intent and rock solid defence.
Worcester now turn their attention to Rotherham Titans on Tuesday as Hill looks for more momentum from his squad ahead of the new Aviva Premiership season in less than two weeks.
The game was delayed by 35 minutes following a motorway accident that delayed the Scarlets arrival at Sixways. And it was Warriors who settled the better with Joe Carlisle narrowly wide from an early penalty from inside his own half.
The visiting lineout was soon being picked apart by Craig Gillies as Worcester starved the Scarlets of attacking platform.
The home pack was repeatedly looking to punch holes in midfield but when they lost possession the Scarlets kicked in behind. Howard was adjudged to have held on under intense pressure, but the resulting penalty from Dan Newton flew wide.
Thumping tackles from Sam Betty and Matavesi rocked the Scarlets back on their heels as they looked to build pressure while Arr almost sent Errie Claassens into space down the wing as the scrum half darted off a scrum down the short side.
Worcester started to turn the screw at the midpoint of the first half and struck after a series of driving lineouts with big Number Eight Semisi Taulava prominent.
A sustained period of pressure finally paid dividends as a delightful disguised pass from Arr sent Matavesi crashing over as the centre picked a superb line to slice through. Carlisle added the extras for a 7-0 lead.
Some slick handling from Matt Mullan and John Andress sent Warriors into clear air to a big ovation before Howard just put a foot in touch as he looked to score in the corner after more neat hands from Carlisle.
Worcester were playing some incisive rugby with ball in hand, but from nowhere the Scarlets cut away down the middle, after a fortunate bounce following a miscued clearance from Jordan Williams, and kept the ball alive.
Warriors looked to regroup and put bodies on the line on the left flank to slow the ball down, but the damage was done as Josh Drauniniu was yellow carded for not releasing after the tackle.
Scarlets immediately looked to make the numerical advantage count but a resilient Worcester defence turned over ball close to the line as Jon Clarke and Matavesi combined before Carlisle boomed a clearing kick to halfway.
Matavesi was impressing as he again flew out of the defensive line and crunched his opposite number to dislodge the ball as Worcester's rearguard continued to hold firm.
A huge hit from Lutui then sent his man tumbling back and opened up space for Chris Jones to sprint away and make a break before recycling to Betty and Taulava. The resulting penalty for offside allowed Carlisle to kick Warriors into a 10-0 half-time lead.
Worcester made a change at the break as Ollie Hayes replaced the hard-working Lutui and the young hooker was soon in the thick of the action as he handed off one man and crashed into contact.
The hosts looked to put width on the ball, but Scarlets almost picked off a looping pass to Drauniniu as they shot out of the line at real pace.
The second try of the afternoon arrived as a high kick caused confusion and, as Scarlets spilled the ball under pressure from Claassens, it was scooped up by Matavesi who streaked away from three men to dive over.
Two soon became three as Claassens handed off his man and broke away to feed Drauniniu on his shoulder. The wing was then alert enough to flip to Arr who put Howard in space to tear over to cap a fluid length of the field move.
Scarlets hit back within two minutes with a well worked score from Reynolds after a break down the left wing was kept alive and continued to push for openings as they refused to let their heads drop.
Hill was now using his bench to give valuable game time to more players with Andy Goode and Ceri Jones were soon exchanging neat passes as Drauniniu skipped inside men with ease and offloaded in the tackle to Nile Dacres.
Worcester continued to try and play an attacking brand of rugby as the game entered the final stages but the final pass just eluded them while Hill gave youth the chance to shine as Academy prospects Max Stelling and Ed Taylor entered the fray.
18m Matavesi t Carlisle c 7-0
40m Carlisle p 10-0
49m Matavesi t Carlisle c 17-0
53m Howard t 22-0
55m Reynolds t Newton c 22-7
Warriors: 01 Matt Mullan (Ceri Jones 60), 02 Aleki Lutui (Hayes 40), 03 John Andress (O'Donnell 57), 04 James Percival (Schofield 57), 05 Craig Gillies, 06 Chris Jones (Dacres 60), 07 Sam Betty (Taylor 76), 08 Semisi Taulava (Kvesic 57), 09 Jonny Arr (Frost 57), 10 Joe Carlisle (Stelling 76), 11 Josh Drauniniu, 12 Josh Matavesi (Goode 60), 13 Jon Clarke (Pennell 54), 14 Ben Howard, 15 Errie Claassens (Nellany 74)
Replacements: 16 Ollie Hayes, 17 Ceri Jones, 18 Rob O'Donnell, 19 Dean Schofield, 20 Matt Kvesic, 21 Niles Dacres, 22 Ed Taylor, 23 Ollie Frost, 24 Andy Goode, 25 Max Stelling, 26 Chris Pennell, 27 Joe Nellany