Arsenal equalled Nottingham Forest's all-time League record sequence of 42 unbeaten matches with a pulsating win.
Thierry Henry gave Arsenal the lead after he lobbed Mark Schwarzer, though Boro contrived an equaliser through Joseph-Desire Job's venomous drive.
Jimmy Floyd Hasselbaink and Franck Queudrue strikes then put Boro 3-1 up.
But Dennis Bergkamp's shot, a Robert Pires tap-in and Reyes' strike - three goals in 11 minutes - rescued Arsenal, with Henry touching home for a fifth.
In a first half, where Arsenal were so completely dominant, Boro's goal lived a charmed life - no more so than in the seventh minute after Schwarzer bravely blocked a Bergkamp shot.
In the ensueing melee Colin Cooper cleared a Frederik Ljungberg shot off the line, while Reyes hit the post.
Reyes then started and got on the end of a flowing Arsenal move but the Spaniard was thwarted by a superb Schwarzer save.
Given such an inspired first-half performance it was only just that Reyes should create Arsenal's opener when, from deep in his own half, he picked out Henry with a raking diagonal pass.
Middlesbrough produced three spectacular strikes
Henry let the ball bounce before calmly guiding the ball over Schwarzer.
Just before the interval Henry came very close to claiming a second when he arched a dipping free-kick over the Boro wall only for the ball to strike the woodwork.
Up to this point Boro's sum contribution to testing the Arsenal defence had been some woeful crosses from Gaizka Mendieta.
But completely against the run of the play Boro snatched a finely-crafted equaliser just before the break.
Queudrue weaved his way towards the Arsenal box, exchanging passes with Hasselbaink, before slipping the ball to Job.
From the tightest of angles the Cameroon international unleashed an unstoppable shot past Jens Lehmann.
Job's goal seemed to convince Boro that Arsenal just might have feet of clay and five minutes after the break the visitors took a surprise lead.
Queudrue was once again involved, replicating Reyes' diagonal pass for Henry's goal, in search of Hasselbaink.
Aided by some clumsy defending from Pascal Cygan and Ashley Cole, Hasselbaink bore down on Lehmann before arrowing a shot past the German goalkeeper.
Three minutes later Highbury was in complete shock as Boro went two goals ahead after Queudrue, noticing Lehmann moving away from his line in expectation of a cross, hit the ball goalwards with the outside of his left foot.
Lehmann was unable to recover his positioning and the ball bent away from him into his bottom right-hand corner.
At this point Arsenal looked to be on their knees but Arsene Wenger's side somehow regrouped to deliver a knockout blow as Boro's defence imploded.
First Bergkamp was allowed to advance to the edge of the box before shooting into the corner.
Then Pires stole in to tap home after good work by Henry before Reyes restored Arsenal's lead with a rising drive, delivered with his right foot.
Late on Henry applied the coup de grace as the French striker touched the ball home.
It was a result that was tough on Boro but showed why Arsenal are now set to surpass Forest's record.
Arsenal: Lehmann, Cole, Cygan, Toure, Lauren,
Ljungberg (Pires 61), Fabregas Soler, Silva,
Reyes (Flamini 78), Bergkamp, Henry.
Subs Not Used: Van Persie, Almunia, Hoyte.
Goals: Henry 25, Bergkamp 54, Reyes 65, Pires 65, Henry 90.
Middlesbrough: Schwarzer, Queudrue, Cooper, Riggott,
Reiziger (Parnaby 74), Boateng, Parlour, Mendieta,
Zenden (Nemeth 78), Hasselbaink, Job.
Subs Not Used: Maccarone, Nash, Doriva.
Goals: Job 43, Hasselbaink 50, Queudrue 53.
Ref: S Dunn (Gloucestershire).