The 26-year-old, who scored a hat-trick in last weekend's 4-1 win over Burnley, starred in a first-half Friday rout as the Europa League semi-finalists established an eight-point gap to 18th-placed Tottenham, who only have five games left to play.
Aided and abetted by a shambolic defensive performance by Regis Le Bris's men, Forest put the game to bed before the kettle for the half-time tea had even been filled.
Trai Hume's unfortunate own goal sparked a spectacular collapse amid which Chris Wood, Gibbs-White and Igor Jesus all scored inside six minutes before Elliot Anderson added a fifth at the death.
In the process, they extended their unbeaten run in all competitions to eight games and inflicted the Black Cats' heaviest defeat since their return to the top flight as they conceded four in successive fixtures, prompting a rare, if mercifully short, chorus of boos at the break.
The result left Tottenham Hotspur and West Ham looking the most likely to be involved in the relegation scrap right until the last day of the season.
"It gives us some breathing room and puts pressure on the two chasing behind," Forest's New Zealand striker Chris Wood said. "Back-to-back wins do that for you.
"We built on the second half from last week, that is what we wanted to do. We want to build and get better and show what we are capable of. We started fast and what we did today was fantastic."
Forest went ahead in slightly fortuitous circumstances with 17 minutes gone.
Omari Hutchinson worked a short corner with Anderson and crossed for Jesus to head the ball against the back of Hume's head, and Robin Roefs could only look on in horror as it flew past him at his near post.
The visitors extended their lead 14 minutes before the break when Roefs's attempted clearance was half-intercepted by Wood, who was on hand to slide the ball into the unguarded net when Gibbs-White played it back to him.
Forest were in dreamland three minutes later when Neco Williams and Anderson worked another short corner for Jesus to head down for Gibbs-White, who thumped a first-time shot past the helpless Roefs.
It was 4-0 with 37 minutes gone when, after Hutchinson's cross had been cleared and Ola Aina's initial attempt blocked, Jesus smashed the rebound home to leave the hosts with a mountain to climb.
Le Bris sent on Reinildo for Rigg at the break and switched to a back three, and they thought they had reduced the deficit when Ballard headed home from close range with 61 minutes gone, only for referee Darren England to be sent to the monitor and ultimately rule out the goal for a foul by Nordi Mukiele on Mat Sels.
It took a sunning one-handed save by Sels three minutes from time to deny Le Fee a consolation goal, and it was Roefs who was picking the ball out of his net once again deep into stoppage time after Anderson arrived perfect on cue to complete the job.
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