Strange had an opportunity to clinch a dramatic victory for the visitors with the very last kick of the game, but his 15m drop-goal attempt was charged down by the Warriors defence.
The defeat was a disappointing result for the 9,000 fans, who had packed the Memorial Stadium for Bristol's last home match before a temporary two-year move to Newport's Rodney Gardens while the ground undergoes development.
Warriors coach Mike Ruddock gave 20-year-old Joe Carlisle his debut and the fly-half had a hand in winger Benjamin's fourth-minute try.
Interview: Bristol head coach Richard Hill
However, Strange punished Worcester's indiscipline and the visitors had former All Black centre Tuitupou to thank for keeping the scores level at 12-12 at half-time.
Worcester found themselves down to 14 men on 50 minutes when Benjamin was sin-binned for preventing the ball from being released, with Strange adding three points from the resulting penalty.
But the yellow card galvanised Worcester - and a slick move saw Gear touch down in the corner, with replacement Drahm adding the extras from the touchline.
Crucially, Strange missed his first kick of the game - and Drahm ensured the result went in Worcester's favour with his match-winning penalty from wide on the left.
Bristol head coach Richard Hill: "I'm extremely disappointed with the result as we wanted to finish at the Memorial Stadium on a high and it would have been perfect if Jason Strange could sign off by kicking that drop-goal to win the game.
"The first half was poor all round. I don't think there was a good Bristol performance in the first 40 minutes at all so I was disappointed with that with the intensity and everything else.
"But in the second half at least we showed a lot of passion, a lot more ambition and produced some lovely breaks. We created numerous chances to finish them off."
Worcester director of rugby Mike Ruddock: "There were three great tries by us but to be fair to Bristol, particularly in the second half, they pressed really hard and created a couple of good opportunities themselves to score tries.
"There was some resolute defence and we showed some passion and pride. We did that little bit extra when the chips were down and our backs were against the wall - that sort of character shone through.
"If we can just improve our discipline which appears to be our biggest problem at the moment. We've talked about it a lot but our discipline let us down and allowed Bristol to keep the scoreboard ticking over."
E-mail this to a friend 
Printable version 
Interview: Bristol head coach Richard Hill
Bookmark with:
What are these?