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Worcester had the better of the set pieces but spilled so many passes they posed little threat in attack.
With six players on World Cup duty and Danny Grewcock suspended, there was a makeshift look about the home side.
Worcester, now under the control of a new director of rugby, Mike Ruddock, also gave first starts to full back Chris Pennell and flanker Tom Woods.
Still to come into the squad however are All Black Rico Gear, Sam Tuitupou and Greg Rawlinson, currently engaged in New Zealand's domestic competition.
Although Worcester took a second-minute lead with a Shane Drahm penalty from 45 metres, Bath were quickly on the counter. A break by fly-half Ryan Davis opened up the visitors' defence but Claasens could not find 6ft 6in left-wing Matt Banahan with the pass.
The opening try was not long in coming however. Claasens finished off Shaun Berne's jinking run and the provider added the conversion on seven minutes.
Drahm missed an even easier chance to kick his second penalty five minutes later but Bath enjoyed most of the possession despite a misfiring lineout. Whenever Worcester did threaten, the final pass went to ground.
Bath added the second try on 17 minutes, working off a scrum and even though centre Tom Cheeseman was taken off the ball, it ran on for Cuthbert to score but Berne was unable to convert.
With the home players seemingly never short of a team-mate in support, Worcester survived a 75-metre counterattack by Nick Abendanon and Davis to strike out of the blue after Banahan was forced to run the ball into touch on the half-hour.
Bath succumbed to a sucker punch as scrum-half Matt Powell took the ball straight from the lineout to run in for a simple try converted by Drahm.
Bath's response was to score a third try on 39 minutes, again by Cuthbert, after Banahan's strong run to the line took out three defenders. With a successful Berne conversion from the touchline, Bath led 19-10 at the break.
Davis was just wide with a 40-metre drop goal attempt on 44 minutes but Worcester, changing to a pick-and-drive game, began to see more of the ball.
Handling frailties continued to undermine their efforts. A couple of minutes later, their best try-scoring chance went begging when Marcel Garvey spilled a pass just short of the Bath line.
After 20 minutes spent in defence, Bath finally roused themselves to force a penalty which Berne converted to make the score 22-10.
Worcester's defence was then tested by Banahan's kick and chase but successfully repulsed Bath's driving maul to secure the scrum put-in. However, they handed Bath the four-try bonus point by losing a strike against the head and the alert Davis put replacement No 8 Browne over for a try converted by Berne. Thinus Delport finally squeezed into the corner for Worcester on 73 minutes but a missed conversion by James Brown still left them two converted tries adrift.
