Higgins, who had previously managed just one top-three finish in more than 200 European Tour events, birdied the 18th to match playing partner Webster's closing 68.
The Tournament was won by French star Julien Quesne - his second European Tour title.
A delighted Higgins said: "I was lucky on the last. I hit an awful tee shot but got a good lie in the fairway bunker.
"You still have to play the shot and I did and got the putt. I haven't had a finish like this in 17 years so I'm delighted."