Boyd marked his 31st birthday by netting his first goals since returning to Rangers and another of Ferguson's former team-mates, Lee McCulloch, also bagged a double.
But young players Lewis Macleod and Fraser Aird were arguably the stars of the show. Macleod notched two impressive finishes with either foot and formed a potent attacking outlet with Lee Wallace down the left, while right-winger Aird scored one and set up two more.
Rangers produced the attacking football that had deserted them in an unconvincing start to the season, which included home defeat by Hearts, and had left manager Ally McCoist facing criticism from fans. Only 11,190 turned up for the second round of a trophy that has so far eluded Rangers.
Ferguson started with a 4-3-3 formation and Rangers quickly looked like they could take advantage of the space in behind, with Aird seeing a powerful early strike stopped by Jamie Barclay following a one-two with Macleod.
The opener came in a 15th-minute counter-attack. Clyde got a number of men forward, but they were in trouble as soon as David Sinclair's blocked shot bounced behind him. Nicky Clark ran at the exposed visiting defence and slid the ball into the right channel for Boyd to slot home.
The second came in the 23rd minute when Barclay could not stop Aird's shot going in off the post after Boyd had left Wallace's cutback following a smart pass from Macleod.
Bilel Mohsni blazed over from six yards before Rangers scored again in the 33rd minute. Macleod latched on to a poor clearance from Scott Durie and his pass was dummied by Boyd, who turned on to Clark's lay-off to finish from six yards.
Aird created two more before the interval, first passing the ball inside to McCulloch to lash high into the net from 18 yards in the 38th minute.
The winger then burst forward before helping the ball towards Macleod, who curled a beautiful strike home from 25 yards in the final minute.
Clyde refused to sit back and try to limit the damage and they enjoyed a decent spell early in the second half without troubling home goalkeeper Steve Simonsen.
But Rangers continued to create chances. Barclay made good saves from Macleod and Aird before stopping McCulloch's shot with his foot.
Nicky Law's chip then came off the inside of the post and Rangers got the sixth in the 65th minute.
Substitute Dean Shiels collected a misplaced pass inside the centre circle before driving forward and releasing Macleod, who drove a left-footed shot into the far corner.
Boyd soon had the ball in the net but was denied by a contentious offside decision following Aird's pass.
However, he claimed his hat trick in the 79th minute when he slotted home following a storming run by substitute David Templeton, two minutes after McCulloch had thundered a 25-yard strike into the top corner.
Rangers finished the game with 10 men after Aird limped off, but only an excellent stop from Barclay denied Boyd his fourth, before Kevin Watt rewarded the away support with a last-minute goal by firing high into the net after a good move down the right.