The Argentina international did not have the mask with him when he scored his only other goal against Peterborough, but it was worth the wait after he produced a mazy run and stunning 61st-minute finish to put the Magpies 4-0 ahead in front of a delighted crowd of 44,464 at St James' Park.
Peter Lovenkrands had earlier struck from the penalty spot a minute before the break and then with a fine header three minutes later as the visitors wilted in the wake of keeper Luke Steele's dismissal.
Danny Guthrie put the result beyond reasonable doubt with a deflected 50th-minute effort, and after Gutierrez's strike, Guthrie made it 5-0 with a free-kick which eluded substitute keeper David Preece, who was then rounded by Kevin Nolan as Newcastle claimed their biggest win of the season.
The game kicked off after a minute's applause for Charlie Crowe, the last surviving member of the club's 1951 FA Cup winning side, and Keith Alexander, following their recent deaths.
Andy Carroll went close to the opening goal 14 minutes before the break when he headed inches wide after Jose Enrique and Fabrice Pancrate had combined superbly down the left.
But the Yorkshire side were dealt a massive blow three minutes later when Steele was dismissed for bringing down Lovenkrands in the box.
The Dane sent Preece the wrong way from the spot to give his side the lead.
Lovenkrands collected his second within three minutes of the restart when Tykes skipper Stephen Foster allowed Carroll to cross for his strike partner, who finished expertly with his head.
It was 3-0 with 50 minutes gone when Danny Guthrie's effort from 22 yards was deflected past Preece, and from that moment on, the only issue was just how wide the margin of victory would be.
Gutierrez's big moment came 11 minutes later when he cut inside from the left before unleashing an unstoppable shot which went in off the underside of the crossbar from just outside the box.
Four became five with 69 minutes gone when Guthrie's free-kick ended up in the back of the net with Carroll desperately claiming he had got a touch, and Kevin Nolan added a sixth two minutes later.
It might have been even worse for the visitors, but Lovenkrands was denied a hat-trick when his 74th-minute header came back off the inside of the post, and Pancrate passed up a glorious opportunity four minutes later.
Substitute Daniel Bogdanovic pulled one back for the visitors after a mix-up between Fabricio Coloccini and Mike Williamson, but the home side might have increased their tally to embarrassing proportions as time ran down.