Fabregas, who now looks back to his best after helping Spain win the World Cup, opened the scoring from the penalty spot after just eight minutes before a quickfire double from Andrey Arshavin and Marouane Chamakh made it 3-0 by half-time.
Arsenal - unbeaten from four Barclays Premier League games and just two points behind leaders Chelsea - kept their foot on the accelerator, with Fabregas heading in number four and substitute Carlos Vela chalking up a late brace.
While sterner tests will lie ahead for Wenger's side, both at home and in Europe, the young Gunners showed again this could just be the season they finally come of age.
Wenger, still with plenty to say about Stuart Attwell's performance in the win over Bolton, had talked about the different style of European refereeing in the build-up to the match.
However, the Gunners boss will no doubt have been just as unimpressed by Luxembourg official Alain Hamer's early decision not to award what appeared a penalty after Fabregas was bundled over by Paulo Cesar in the opening exchanges.
Arsenal, though, were soon in full flow as Fabregas released Jack Wilshere into the Braga box, only for the youngster to be halted by a marginal offside flag.
The hosts, however, did not have to wait long to take the lead.
Fabregas was again the creator, slipping Chamakh ahead of the static Braga backline.
The Moroccan, who has impressed since his summer arrival on a free transfer from Bordeaux, sidestepped keeper Felipe, only to be brought crashing down.
The Arsenal captain stepped up to dispatch the resulting penalty - celebrating his first goal of a season which could well have started at Barcelona by kissing the badge in front of the Clock End faithful.
It was almost 2-0 moments later when Arshavin combined with Fabregas to tee up Wilshere, but his close-range shot was well saved.
Braga - nicknamed 'Arsenal do Minho' because the clubs share the same home colours - boasted six Brazilians in their XI, although none had a full international cap.
Nevertheless, a team which had knocked out both Celtic and experienced campaigners Sevilla en route to Europe's elite for the first time deserved some respect.
Cesar's deflected effort forced Arsenal keeper Manuel Almunia to make a reaction save, before Alan scampered away down the right ahead of Fabregas but his low cross flew through the six-yard box.
Slowly, Arsenal began to get back on top and it was no surprise when Arshavin made it 2-0 on the half-hour.
The Russian had missed some straightforward chances against Bolton, but made no mistake this time when driving an angled shot under the keeper after being played into the left side of the Braga penalty area.
Before the visitors could regroup, they were further behind.
Another sweeping Arsenal move saw the ball worked across field and to the edge of the 18-yard box. Arshavin's chip picked out Chamakh, who played a neat one-two with Wilshere and swept the ball into the net.
The interval offered little respite to Braga, who went 4-0 down at the start of the second half when Fabregas headed in Arshavin's chip to the far post.
The Gunners captain was then denied a hat-trick by the deftest of touches from keeper Felipe and an acrobatic goalline clearance by Moises.
As the hour mark passed, and with one eye on Saturday's trip to Sunderland, Wenger replaced Chamakh and defensive midfielder Alex Song, as Vela and Denilson came on.
Arsenal remained dominant as Arshavin rattled the base of the post with a fierce angled drive, this time cutting in from the right.
The Russian then unselfishly played in Vela, who dispatched a neat chip into the far corner for his second goal in as many games.
Arshavin was also given a break, Emmanuel Eboue coming on for the final 20 minutes, as the Gunners coasted to another impressive victory, with Fabregas setting up Vela to slot home number six five minutes from time.