A winner on his chasing debut at Ascot in December before following up at Musselburgh on New Year's Day, the Paul Nicholls-trained six-year-old was the 2-5 favourite to complete his hat-trick in the Racing To School Riders' Programme Novices' Chase.
With just two rivals in opposition, Cobden sent Greaneteen straight to the lead and a slick round of jumping kept the pressure on the chasing pair.
Champagne Mystery attempted to bridge the gap in the straight, but Greaneteen never looked in any danger of being caught and passed the post five lengths to the good.
Cobden told Sky Sports Racing: "They're quite trappy fences around here and he came out of my hands a couple of times and put me back in my place!
"He's a pleasure to ride and he's actually a very good horse. It's nice for Chris Giles (owner) to have a good one."
Greaneteen holds an entry in the Arkle Trophy at next month's Cheltenham Festival and now qualifies for handicaps, bringing the Grand Annual into the equation.
However, Cobden feels he could sidestep the showpiece meeting in the Cotswolds entirely.
He added: "I'd like to see him do something at Aintree. He hasn't got that much experience, although he's so good (at jumping). We could go to Aintree and possibly have one more run between now and then, or go straight there.
"Paul is the master of placing them - I'm only a schoolboy. I do rate this horse quite highly."