Worcester, in 11th place before kick-off with only two wins from eight league starts, dominated territory and possession to leave Bath living off scraps.
Wing Miles Benjamin scored a superb solo try for the Warriors, while fly-half Joe Carlisle chipped in through two penalties and a conversion before Andy Goode added a drop-goal six minutes from time.
The win moved Worcester nine points above bottom club Newcastle, who visit unbeaten league leaders Harlequins on Sunday.
Bath managed a 69th-minute touchdown for prop Charlie Beech after he was driven over from close range - substitute Olly Barkley converted - yet it proved too little too late.
Moody, his trademark all-action style making little headway in a Bath side devoid of ideas, lasted only 49 minutes before injury forced him off.
And to complete a miserable night for Bath, their England lock Dave Attwood was carried off with his neck in a brace following a lengthy stoppage midway through the second period while medical staff stabilised him.
Moody finished second-best after attempting to tackle Worcester wing Marcel Garvey just before half-time, departing for treatment before making a brief return that he eventually aborted.
Only two days ago, Moody felt obliged to issue a strongly-worded statement hitting back at suggestions he put commercial gain before his rugby during England's dismal World Cup campaign.
Rugby Football Union elite rugby director Rob Andrew reportedly criticised Moody for leading a senior player delegation that disputed the squad's World Cup payments.
Moody was also targeted by one unnamed team-mate for having too much contact with his agent during the tournament, the claims being made in post-World Cup reports leaked to a national newspaper.
The 33-year-old at least attempted to do his talking on the pitch after a day when he also had a £10,000 RFU fine reduced by £2,500 for breaching World Cup commercial rules when he wore a sponsored mouthguard in New Zealand.
But it all proved to no avail as Bath lacked the basic skills and organisation to seriously threaten a victory that would have lifted them into title play-off territory.
Carlisle missed an easy opening penalty chance, and although he opened Worcester's account through a 10th-minute strike, his opposite number Stephen Donald also suffered a wayward first half off the tee.
Donald sent two penalties wide during a 13-minute spell, and Bath continued to struggle, hardly helped by a misfiring lineout caused in no small measure by prop Mark Lilley being pressed into emergency hooking duty with Lee Mears, Pieter Dixon and Ross Batty all injured.
A bloodied Moody exited four minutes before the break, and Warriors took advantage in emphatic fashion.
Just when a dire opening 40 minutes appeared to be petering out, the home side conjured a memorable try that split Bath's defence asunder.
Carlisle delivered a superbly-timed pass to Benjamin, and the England Saxons player finished brilliantly as he weaved his way over from 30 metres out.
Carlisle added the conversion and Worcester trooped off with a commanding 10-0 interval lead against opponents that offered next to nothing in attack.
Bath offered glimpses of what they could do as the game began to break up, but poor passing let them down and another Carlisle penalty extended Worcester's advantage.
The visitors also floundered on a ferociously committed Worcester defence, at times battering away through phase after phase without crossing their line.
Beech eventually got the scoreboard moving for Bath, yet Worcester quickly regained a territorial foothold and Goode's late drop-goal not only confirmed Warriors' triumph but also denied their opponents a losing bonus point.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.