Ex-international duo Ashwell Prince (95) and Simon Katich (84) had helped the Red Rose gain a first-innings lead of 114 by underpinning a score of 448 for seven declared just after lunch.
Worcestershire were then reduced to 17 for one in the ninth over of their second innings, but rain arrived for the third day running with the score at 26 for one.
At Chelmsford, Tom Westley continued his impressive start to the season as Essex's match against Gloucestershire ended in an inevitable draw.
In a contest ruined by the weather - 156 overs were lost because of rain and bad light - Essex finished on 353 for six in reply to a visiting total of 409 for five declared.
But Westley will look back on the game with immense satisfaction. The 24-year-old opener scored 163 - an effort that followed innings of 58 and 133 against Cambridge UCCE a week ago and confirmed his rich promise.
The two other games - Northamptonshire's home match with Glamorgan and Leicestershire's trip to Hampshire - were both washed out without any play.
- Sports & Recreation
- Tom Westley
- Simon Katich