Batting first, Lancashire reached a healthy 248 for five in 50 overs with handsome contributions from Stuart Law (70 off 62 balls) and Mal Loye (64).
Zaheer was far from impressive and he conceded 55 runs in his 10 overs, which also included a maiden.
In reply, Worcestershire were never in the hunt, losing wickets at regular intervals and Tom Smith took the game away from them, claiming three wickets. Smith's triple strike removed Stephen Davies, Gareth Batty and Roger Sillence as Worcestershire slumped to 74 for seven and they were all out for 129 in the 43rd over, conceding a 119-run defeat.
Zaheer's contribution with the bat was 13 from 17 balls with two boundaries in it before Sajid Mahmood got the better of his defence.
In another match, Dinesh Mongia Mongia claimed a wicket and then remained not out on two as Leicestershire recorded their first C&G Trophy win of the summer, beating Warwickshire by seven wickets in a rain-plagued match at Grace Road.
Warwickshire reached 128 for nine as seamer James Allenby took four for 19, Pakistani pacer Mohammad Asif claimed two and Mongia scalped one. After rain forced the Duckworth-Lewis system, the target was reduced to 116 off 30 overs and Leicestershire had sedate start with openers Darren Maddy (53) and Darren Robinson (47) adding 104 before three wickets fell for just two runs.
Mongia (2 not out) and John Maunders (7 not out) completed the formalities as Leicestershire reached 116 for three in 22.4 overs.
Darren Maddy's 53 included a six and six hits to the fence.