Miley got the opener for the home side, before Miguel Almiron and Dan Burn put some gloss on proceedings as Newcastle win at home in the league once again.
The result comes as a huge relief for Newcastle's injury-hit squad, after three straight defeats across all competitions in the past week-and-a-half.
After an even opening 20 minutes, Fulham were given a mountain to climb when striker Raul Jimenez was sent off for an erratic lunge on Sean Longstaff.
It was largely one-way traffic from there on in, but it took until the second half for Eddie Howe's side to make the breakthrough, when Miley scored his maiden senior goal.
Almiron netted just over five minutes later to put the game out of reach for the 10 men of Fulham, with Burn adding another late on, as the hosts win a seventh straight home Premier League game.
Shortly before turning into the villain, Jimenez had the first moment of note, when the man in-form attempted an audacious overhead kick from 25 yards out, and even though the Mexican did well to keep his effort on target, it never troubled Martin Dubravka in the Newcastle goal.
Both sides had half-chances shortly after, as Harry Wilson broke in behind the Newcastle backline, but could not find anyone with his square ball, before Bruno Guimaraes blazed over from Anthony Gordon's cutback.
It was on 20 minutes when the game's flashpoint came though, as Jimenez was penalised for a wild challenge on Longstaff, which saw the Fulham man clatter his opposite number in the face with his hip.
Jimenez was initially only given a yellow card, but after a brief VAR review, referee Samuel Barrott dished out a straight red card.
After already having Fabian Schar forced off with a hamstring injury early on, Howe was dealt yet another blow as Joelinton was also replaced with what appeared to be a muscular issue shortly before half time.
Despite that setback though, Newcastle dominated the remainder of the first half given their man advantage, with Gordon going closest, striking the crossbar from a tight angle, with Longstaff in disbelief that he was unable to steer the rebound home.
Longstaff once again found himself in excellent position soon after, but after taking too long to get a shot away, Bernd Leno was able to rush out and smother the attempt.
Fulham remained competitive and ventured forward whenever possible, and manager Marco Silva will have been furious that Alex Iwobi was unable to make more of a Newcastle mistake that saw him played through on goal, but he shot straight at Dubravka, as the sides went in goalless at half time.
The second half followed a similar pattern, with territorial dominance for the hosts, and after Gordon and Miley both tested Leno early after the interval, the deadlock was finally broken.
Following a fortunate ricochet off both Guimaraes and Antonee Robinson, the ball fell kindly for Miley in the area, and the 17-year-old showed great composure to drill his effort low into the corner beyond Leno to give Newcastle the lead.
Barely five minutes had passed before the Magpies added a second, with Gordon instrumental in the build up, threading a pass through for Callum Wilson, who was bundled over in the area by Robinson, but that allowed the ball to run through for Almiron, and the Paraguayan gleefully accepted the easiest finish he will have all season.
As Howe's side were seeing the game out professionally with little fuss, there was time for Burn to get in on the act, as a wonderful outside-of-the-foot cross from Guimaraes found the huge defender, and despite a remarkable initial save by Leno, the ball bounced back off the Newcastle man and into the net.
A frustrating day personally for Wilson in attack was compounded deep into stoppage time, as the striker saw his effort cannon back off the post, but Newcastle were soon able to celebrate a comfortable 3-0 success.
Both sides are in the EFL Cup quarter-final action in midweek, before returning to league matters next weekend, with Newcastle going to Chelsea, and Fulham facing Everton at Goodison Park.