The victory was Glamorgan's first over Worcestershire at their Cardiff headquarters for 42 years. The Australian-born Allenby followed up his top score of 78 in Glamorgan's first innings to claim figures of four for 27 in 20 overs in the Worcestershire second innings.
He helped himself to three wickets on the final morning as the Welsh county claimed the final five wickets for only 22 runs after Worcestershire resumed on 185 for five to leave 36 for victory.
In reply to Worcestershire's 207 all out opener Ben Wright led the way in with 30 of the runs required as Glamorgan won 35 minutes before lunch.
Glamorgan took 21 points from the contest to Worcestershire's three.
The visitors did not make the start they required when Sri Lanka star Thilan Samaraweera was caught and bowled by Michael Hogan for 79 in the fifth over of the day. And in the next over wicketkeeper Michael Johnson was caught by Marcus North off the potent bowling of Allenby.
It left Worcestershire in trouble at 195 for seven, a lead of only 23.
Bowling with the second new ball Allenby was on target again, breaking through twice in the same over.
First he bowled David Lucas to uproot his off stump before trapping Chris Russell leg before.
Hogan claimed the last wicket to fall by having Gareth Andrew caught by North at mid-off.
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