But getting over the winning line seemed a long way away when David Wheeldon was caught down the legside by wicketkeeper Jonathan Batty off Gemaal Hussain with only one added to their overnight total.
Mitchell and Solanki steadied the nerves before Gloucestershire fought their way back into the game.
Chris Taylor pulled off a stunning catch at mid-wicket to remove Solanki before Bangladesh all-rounder Shakib Al Hasan needlessly holed out to Will Porterfield.
Bit Moeen and Mitchell then came together to put the game out of the hosts' reach, with Mitchell completing his second ton of the match off 218 balls, with 10 fours.
Worcestershire director of cricket Steve Rhodes told BBC Hereford and Worcester: "To get two hundreds in a game and to be not out in the second one when chasing 339 was just outstanding from Daryl Mitchell.
"He has played well for the last two or three weeks and he maximised what was a good wicket but in some difficult conditions.
"The new ball for one thing made it hard but also the spinners bowling into the rough, but he played admirably."
Bookmark with:
What are these?