Luton captain Scott Cuthbert was shown a straight red-card in stoppage time for bringing down McLeod, allowing substitute Noble to take the headlines by crashing a free-kick into the top corner from 20 yards give Notts a first home win in Sky Bet League Two.
Ricardo Moniz made two changes to the team which started the Johnstone's Paint Trophy victory against Mansfield with Roy Carroll and Mawouna Amevor returning from international duty to take the places of Scott Loach, who dropped to the bench, and Wes Atkinson.
Curtis Thompson was fit enough to make the bench following a month out with an injury and Noble was named among the substitutes after serving a three-game ban.
Luton had applied early pressure, but a quick break from a visiting corner gave Notts their first sight of goal as Jon Stead, Adam Campbell and Genaro Snijders combined to send McLeod haring away down the left wing. The striker cut inside and curled a shot towards the top corner which was held comfortably by Tyler.
McLeod was then denied a stone-wall penalty after being tripped by Stephen O'Donnell as he advanced into the penalty area. To add insult to injury, the striker was booked for the supposed indiscretion.
Danny Green stung the palms of Carroll with a powerful free-kick on the corner of the penalty area for John Still's side and Burke did well to block a goalbound effort from Ollie Lee.
Incisive, one-touch football saw Notts carve Luton open with McLeod rolling the ball across the face of goal, where it was cleared by Scott Cuthbert. Snijders was waiting behind the defender to pounce on any error to open the scoring.
Notts thought they had the opening goal as Burke's free-kick was bundled home, seemingly by a Luton defender. However, the celebrations were cut short as the linesman's flag was up for offside.
The first goal finally arrived shortly after the half-mark and it was no surprise to see it go in Notts' favour given their superiority and commanding performance.
Burke was given too much time and space to send a perfectly-flighted cross to the far post where McLeod headed back across goal and into the far corner in front of the Kop.
Not satisfied with their work, Notts continued to lay siege to the Luton goal. Snijders collected the ball in midfield and rode a couple of challenges before rifling narrowly past the upright from 20 yards.
The lead was doubled just a few minutes into the second half. Thierry Audel burst forward from left back and played a defence-splitting pass to put McLeod in one-on-one with Tyler. The striker, full of confidence, simply clipped the ball over the goalkeeper into the far corner for his third goal in two games.
Campbell curled over from the edge of the area before Burke's raking 60-yard pass was just out of reach for the hat-trick hunting McLeod.
Although County had looked comfortable, Luton brought themselves back into the game when Scott Griffiths' cross found Craig Mackail-Smith, who slipped the ball to substitute McGeehan to beat Carroll at the near post.
Another Burke pass gave Campbell a scoring chance only to see his shot smothered by Tyler, making the former Newcastle striker wait for his first goal in the black and white stripes.
That profligacy was punished immediately by the visitors. Smith was allowed to take aim from 25 yards and he made no mistake in finding the bottom corner to equalise.
The Magpies thought they had found a winning goal when Noble wriggled his way through the area and squared for Burke to tap in from a few yards out but the offside flag again denied Moniz's team before Mackail-Smith smacked a shot wide at the other end as Luton remained a threat on the counter-attack.
But the game swung back Notts' way in stoppage time as Cuthbert was sent off for hauling down McLeod 20 yards from goal.
Following a lengthy delay, Noble took responsibility for the free-kick and unleashed an unstoppable shot which was past Tyler before the goalkeeper could move as Meadow Lane erupted with joy, delight and relief.
Notts: Carroll; Amevor (Edwards 85), Swerts, Hollis, Audel; Aborah, Burke; Snijders (Jenner, 79), Stead, Campbell (Noble, 85); McLeod.
Subs not used: Loach, Smith, Thompson, Spencer.
Attendance: 5,820 (1,689 away)