Spanish rider Barreda won the 457km Bisha to Wadi Ad-Dawasir test by three minutes, 55 seconds ahead of defending champion and Honda teammate Ricky Brabec, as the pair bounced back from a difficult first stage of the rally.
Barreda led at every single waypoint en route to a success that ties him with five-time event winner Marc Coma for fourth on the all-time stage wins list.
Having gone into the day down in 18th and trailing by 14 minutes and 21 seconds, Barreda now leads the standings overall by 6m23s ahead of Brabec.
Pablo Quintanilla was third-fastest on the stage for Husqvarna, 6m02s down on Barreda, followed by top Yamaha rider Ross Branch and another Honda rider, Jose Ignacio Cornejo.
Branch, a newcomer to the Yamaha squad for this year, now sits third overall, just 14s behind Brabec, while Quintanilla is fourth ahead of fellow Husqvarna rider Xavier de Soultrait.
KTM's trio of factory riders all dropped down the leaderboard on a day to forget for the Austrian marque, with 2018 race winner Matthias Walkner suffering the worst.
Walkner had begun the day third but suffered an early clutch problem that cost him two hours and 15 minutes, and has plummeted to 46th in the overall classification.
Sunday's stage winner and overnight leader Toby Price meanwhile steadily lost time to Barreda throughout the stage and ended up giving away 32 minutes to the Spaniard - leaving him 17m39s off the lead and provisionally 16th in the standings.
Sam Sunderland fared slightly better but still failed to crack the top 10 on the stage as he lost 23 minutes, leaving him 12th provisionally and 12m50s down on Barreda overall.
KTM rookie Daniel Sanders was second behind Barreda at one point in the stage, but lost ground in the final part of the test and ended up ninth, 16 minutes down at the finish.
Also having a tough day was Stage 1 runner-up Kevin Benavides, who has slipped to 13th overall after losing almost 29 minutes to Honda teammate Barreda.
Yamaha's Andrew Short has become the first factory team retirement of the rally following an unrepairable mechanical issue.
In the quads category, Pablo Copetti took the stage win by 1m03s by Giovanni Enrico, but Alexandre Giroud still leads overall by 1m09s from Enrico.
Standings after Stage 2 (top 10):
Xavier de Soultrait
Adrien van Beveren