Former Lothians champion Miller beat Craig Davidson at the 19th in the deciding match to deny Craigielaw a first title triumph in the event.
The East Lothian club had three putts to win this season’s decider at Bruntsfield Links before Duddingston eventually came out on top 5-4.
“Duddingston Golf Club should be very proud of the boys this season,” said team manager Gordon Milligan.
“We won the South East Winter League, narrowly lost in the final of the Edinburgh Inter Club and now this victory extends our lead to two from Royal Burgess in the Summer League.”
Duddingston were without Craig Pirie, who tested positive for Covid-19 on Thursday morning but sent his team-mates a ‘good luck’ video, which they watched over breakfast at Bruntsfield.
Scottish champion Angus Carrick was also a notable absentee for Craigielaw due to the fact he was meeting up with his Scotland team-mates for this week’s Home Internationals at Hankley Common.
Club champion Andy Fairbairn drew first blood for Duddingston, covering the 14 holes played in three-under as he beat Kenny Glen, who’d helped Lothians win the Scottish Area Team Championship the previous weekend, 5&4.
The match behind between Miller and Davidson produced good golf throughout, the pair trading birdie blows on the back nine and eventually finishing all square after 18.
Davidson, one of Craigielaw’s star performers this season, had narrowly missed birdie putts at 16th and 17th before rolling in a six-footer on the last after his opponent had missed from 15 feet.
Uncharacteristically, Duddy’s Ryan Buckley had a bad day on the greens as he went down 2&1
to Ross Colquhoun before Craigielaw moved 3.5-1.5 ahead thanks to that success being backed up by wins from Dan White and Dave Nicolson.
White survived losing the 15th, 16th and 17th holes to beat Gary Thomson on the last green while former Duddingston member Nicolson edged Mike Armstrong 2&1 in another tight tussle.
“I was still fairly confident at this point as we were in command of the final four matches,” said Milligan, who was pleased to then see the score levelled up again after the next two matches had been completed.
Davie Downing, who had been drafted in as Pirie’s replacement, beat Lewis Reid 3&2 before five-time club champion Derrick Williams shrugged off a wrist problem to beat Craigielaw team captain Rodney French 2&1.
“We still appeared to be in control of the final two matches, however things were about to change,” said Milligan of what happened next.
Jamie Duiguid, who had been up two up with four to play, lost the 15th and 16th then was unable to convert a 12-foot birdie putt at the last as he had to settle for a half with Guy Dalziel.
Then, in the anchor match with a big crowd looking on, after being in command early on Ben Alexander found himself one down with two to play against Mark Watt.
It would have been Craigielaw’s crown if Watt had been able to two-putt at the 17th, but, after running his first one three feet past the hole, he then missed a short one for glory.
Doing well to compose himself, Watt then hit a great bunker shot at the last to around eight feet, but the putter let him down again as that chance went begging to mean Miller and Davidson headed out for extra holes.
Davidson, who had driven the ball great all day, snapped hooked and went out of bounds, leading Miller to switch to a 5-wood for his tee shot.
The current Royal Burgess champion then hit a 6 iron just short of the green, pitched stone dead and it was job done for Duddingston.
Craigielaw 4, Duddingston 5
(Craigielaw names first)
Kenny Glen lost to Andy Fairbairn 5&4
Craig Davidson lost to David Miller at 19thRoss Colquhoun bt Ryan Buckley 2&1
Dan White bt Gary Thomson 1 hole
Dave Nicolson bt Mike Armstrong 2&1
Lewis Reid lost to Dave Downie 3&2
Rodney French lost to Derrick Williams 2&1
Guy Dalziel halved with Jamie Duguid
Mark Watt halved with Ben Alexander