Gordon Strachan's men came into the clash as strong favourites against the minnows, but became the first side to concede a competitive goal to Gibraltar when Lee Casciaro cancelled out Shaun Maloney's earlier penalty.
Casciaro, a policeman back in his homeland, placed a low shot beyond the advancing David Marshall as Gibraltar's wait for a first goal in qualifying was ended.
Gibraltar were level for less than 10 minutes, however, as Scotland found another gear and netted three times in quick succession prior to the interval.
Fletcher scored his first international goal in almost six years with a scrappy header, before hero Casciaro turned villain with a foul on Steven Naismith and Maloney successfully converted his second spot-kick.
Naismith got in on the act soon afterwards with a first-time finish as Scotland pulled further clear, and Fletcher rounded off the scoring with two more goals in the second half as Strachan's side made it 10 points from five Group D games.
Gibraltar, meanwhile, will at least be buoyed by breaking their competitive goal duck, which was almost ended in the eighth minute when Marshall clawed the ball away as Joseph Chipolina's cross from the left threatened to drift in at the near post.
Scotland nerves were briefly settled 10 minutes later as Maloney calmly converted a spot-kick having been felled by goalkeeper Jamie Robba.
It was a needless foul by Robba with Maloney running towards the byline, and the winger punished him by sending his kick into the bottom left corner.
Scotland's lead lasted just a minute, however, as Aaron Payas released Casciaro, who showed great composure to drill a low finish through the legs of Marshall, sparking scenes of jubilation among the Gibraltar players and fans in the crowd.
Stunned by that equaliser, the hosts went back on the attack and scored three times in 10 minutes before the break.
Fletcher restored their lead in the 29th minute as his header crept in after Gibraltar failed to deal with Ikechi Anya's cross and then Casciaro's clumsy challenge on Naismith allowed Maloney to double his tally with another penalty, which also went to the keeper's right.
The post kept out Fletcher's clever flick before Anya got in down the left and cut the ball back for Naismith to sweep home as Gibraltar wilted under the pressure.
Fletcher ought to have netted his second on the hour mark, but he failed to get a telling touch on Alan Hutton's inviting cross from the right.
The Sunderland striker made no mistake 17 minutes later, however, rising to nod in substitute Jordan Rhodes' delivery from the same flank. A calm left-footed finish a minute from time sealed his hat-trick.
It marked a welcome return to form for the forward, who had not found the net in any competition since November, as Scotland completed a convincing victory.
