The Jamaica international fired home from 18 yards in the 53rd minute as Motherwell strengthened their grip on third place in the Clydesdale Bank Premier League.
Scott Vernon had quickly levelled after Michael Higdon headed the visitors into an early lead but Aberdeen rarely looked like equalising again.
Aberdeen have now failed to beat Motherwell in eight games since Mark McGhee departed Fir Park to take over at Pittodrie in 2009, with Brown faring even worse than his predecessor against his former club.
The victory, and the winning goal in particular, was a tactical triumph for Stuart McCall, who changed his formation to accommodate Daley for his first start since joining the club in September.
Daley played up front alongside Higdon with Murphy in the hole behind, and the plan worked to perfection as the former Scotland Under-21 international set up the crucial strike.
Aberdeen, who were without the suspended Rory Fallon and injured Kari Arnason, had won consecutive home games against Dunfermline and Dundee United before narrow defeats against the Old Firm, but they struggled for creativity, although Mohamed Chalali hit the bar just before Daley's goal.
The Dons had not played for three weeks after their match at St Johnstone was postponed before the international break and they were caught cold in the fifth minute.
Rory McArdle gave away a needless free-kick near the corner flag for a foul on Nicky Law, who had already lost the ball. Tom Hateley swung the ball in to the near post and Higdon glanced the ball home.
The lead only lasted five minutes as Aberdeen scored from their first meaningful attack.
The Dons worked the ball to Rob Milsom on the left wing and he swung the ball in quickly before the away defence could shape up. Vernon was unmarked six yards out and he headed the ball down and past the legs of Darren Randolph.
Aberdeen took confidence from the goal and pressed for another, and Chris Clark curled not far over from 25 yards.
Motherwell regained control of possession for a spell but they could make no inroads in the final third, and Vernon had another headed chance five minutes before the break when Fraser Fyvie's inswinging free-kick found him 12 yards out but he could not make a clean connection.
Motherwell dominated possession just after the restart but Aberdeen forced the ball off them to create the first chance of the half.
Once again an early cross caused problems as Rory McArdle delivered from the right and Chalali headed the ball off the top of the bar from 15 yards.
The visitors went straight up the park and regained the lead.
Murphy hooked a bouncing ball over the top of the Dons defence for Daley to run on to. The former Bradford player had Law outside him but he checked back on the edge of the box and shot past two Dons defenders and goalkeeper David Gonzalez into the bottom corner.
Chalali threatened again with a powerful 25-yard strike that Randolph parried wide at full stretch but Aberdeen, with Peter Pawlett on for Clark, could not break Motherwell down despite pushing them back at times.
Chris Humphrey replaced Daley and gave Motherwell a good outlet on the right wing to relieve the pressure.
And the home fans' frustration grew as centre-back Youl Mawene found himself the furthest man forward after winning possession 30 yards from his goal following a Motherwell corner.
The move broke down just inside the Motherwell half and the visitors defended in numbers when they had to while continuing to break forward whenever the chance arose to seal their sixth away win of the season.