The British No 1 beat the American earlier this month as Great Britain defeated the USA in the Davis Cup and he followed that up by prevailing in one hour and 22 minutes.
Murray needed four sets to see off the world No 44 in Glasgow, but he was rarely troubled this time by Young on the Stadium Court as he booked a clash with either Colombia???s Santiago Giraldo or Dutchman Robin Haase.
The Scot is seeking his third Miami triumph after lifting the title in 2009 and 2012.
Murray had only lost once to Young in their??previous five meetings and he got off to a blistering start, breaking the??American’s serve twice and holding his own to claim an early 4-0 lead.
The third seed looked on course for a whitewash first set when he opened up another two??break points in the fifth game but Young then found his form.
The 25-year-old left-hander seemed to grow in confidence as he capitalised on??some windy conditions and an incorrect Murray challenge to break back, winning??three consecutive games to trail only 5-4.
Murray cut a frustrated figure but he recovered his composure to serve out the??first set, before claiming a break in the opening game of the second.
Young tested his opponent with an aggressive forehand but his hitting was too??straight and too inconsistent to build any sustained pressure.
A superb backhand pass gave Murray another break point at 3-1 and while Young??held off temporarily, the Scot took advantage two points later to take a??three-game lead.
Unforced errors continued to undermine Young’s slim hopes of a fightback and??while he pulled another game back to make it 5-2, Murray served out to seal a??comfortable victory.