The Tasmanian allrounder had already made the highest score of the County Championship match on a tricky pitch at Edgbaston, his second innings' 91 enabling the Bears to set visitors Essex a challenging 206 to win.
With veteran Keith Barker (4-28) taking a triple-wicket maiden in Monday's second over to rip through Essex's upper order it seemed Webster's bowling would not be required, bar a couple of early wicketless overs.
Resuming on Monday morning at 0-11 Essex had lost South African opener Dean Elgar lbw playing no stroke for a duck and were quickly struggling at 4-21.
Another South African, youngster Luc Benkenstein, engineered a minor recovery, but when he went for 39 Essex were 7-82.
However, with Simon Harmer digging in to take Essex to 8-163, assisted by Zaman Akhter, Webster was given the ball again. With the partnership up to 51 he did the trick with the seventh ball of his second spell, inducing an edge from Harmer (32) that was well taken at second slip.
He followed up by having Akhter (35) caught on the boundary attempting a ramp, to seal a 41-run win.
Jake Lehmann was less fortunate, his batting efforts proving in vain as Hampshire lost by two wickets to Somerset at Southampton.
Lehmann had made twin half-centuries as Hants set the visitors 286 to win, but though England prospect Sonny Baker took 5-62 Tom Abell took Somerset to victory.
The veteran marshalled the tail superbly, ultimately hitting a boundary in mid-afternoon that both secured victory and brought up his hundred.
In Division Two James Anderson finished with match figures of 7-63 as Lancashire, set 202, wrapped up a four-wicket win over Cameron Bancroft's Gloucestershire at Bristol.
This was despite a rare double failure by Marcus Harris, who followed a first innings 11 with a three-ball duck in the second dig.
"Jimmy Anderson has still got it and presents a real challenge with the new ball," said Bancroft of the 43-year-old.
At Northampton Sydney-born former England opener Sam Robson made 162 as Middlesex secured a draw against Darren Lehmann's Northamptonshire.
Aussie trio Harry Conway (0-17), Liam Guthrie (1-89) and batting centurion Nathan McSweeney (0-17) all had a bowl, and while Guthrie eventually got Robson the chance of a positive result had long gone.
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