But spinners Ian Blackwell (3-67) and Scott Borthwick (3-25) shared six of the eight wickets to fall as Worcestershire were all out for 213.
Durham finish third in the table, with Worcestershire seventh.
BBC Hereford and Worcester's Trevor Owens:
"After a bright start to the final day in which James Cameron and Moeen Ali added 63 for the third wicket, Worcestershire rather fell away.
"Given they had secured their first division status on the third day, there was always a danger of 'After the Lord Mayor's Show' and the coaching staff admitted there was certainly an element of this in the batting display.
"But, despite this being their 11th defeat in 16 County Championship matches, Worcestershire have done enough to remain in Division One and this defeat does little to detract from this achievement, achieved very much against the odds."
Durham head coach Geoff Cook told BBC Newcastle:
"It's a nice thing to take into the winter, especially when the team played really well in the last two four-day matches.
"We were outstanding down at Sussex, and this performance when we had a very small chance of winning the Championship, I thought the players were excellent.
"They batted under tough conditions on a little bit of a wearing wicket, and if we had got some more batting points we might have had a chance.
"Worcester played very well, they were a credit in tough bowling conditions and gale force wind and the discipline they showed they made life very tough for us."
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