Stuart Armstrong's close-range finish gave the hosts the opener at St. Mary's but Wood’s superb header from Jonjo Shelvey's cross drew the Magpies level before the break.
Six minutes into the second period, Guimarães – who was making his first start for the club since joining from Lyon in January – produced a sensational strike, backheeling United into the lead.
And it was an advantage they refused to relinquish, as the visitors held on to extend their unbeaten run in the Premier League to nine games.
With Joelinton missing through injury head coach Howe handed a full debut to fellow Brazilian midfielder Guimarães, who has had to be patient since making the switch from Ligue 1, with Wood again leading the line for the upwardly-mobile Newcastle.
Guimarães' inclusion was the only change from the United side which beat Brighton 2-1 at the weekend, but once a cagey opening gave way to an end-to-end contest in the first half, it was Ralph Hasenhuttl’s Saints who seized the advantage.
Southampton had already fired a warning midway through the first period, with Armando Broja blasting Moi Elyounoussi’s through ball just over after Shelvey had been robbed of possession in midfield. Just a couple of minutes later, they did make a breakthrough; Kyle Walker-Peters' cross from the left was nodded back into the middle by Elyounoussi and Scotland international Armstrong was there to apply the finishing touch, despite Dan Burn’s best efforts.
But the Saints' lead lasted just seven minutes. It was a terrific leveller from the Magpies, whose patience and neat play on the left flank was rewarded when Shelvey swung in a fine cross towards Wood, who dispatched his header with aplomb, leaving former Newcastle goalkeeper Fraser Forster rooted to the spot.
The New Zealand frontman's debut strike in black and white opened the game up a little, with Newcastle forced to dig in to remain on level terms as Che Adams' thumping effort rattled the crossbar before the break, with Martin Dúbravka beaten.
Seven minutes after the restart, though, the game’s defining moment arrived. Former Southampton full back Matt Targett - a Saints fan who came through the ranks at St. Mary’s - swung a corner in from the right and Burn, solid in defence once again, nodded it in back across goal. Then it was all about the improvisation of Guimarães, whose sensational volleyed backheel flashed past Forster and into the roof of the net, sending the travelling United supporters – who were situated behind that goal – wild.
The goal rallied Newcastle, with Targett seeing a powerful effort blocked by Mohammed Salisu on its way to goal before Guimarães' evening ended slightly early as he was withdrawn with a knock with a quarter of the contest still to go.
After Fraser had tested Forster from range, the hosts applied plenty of pressure as they looked for an equaliser. Tino Livramento's looping cross required an intervention from Dúbravka, who then stopped a Salisu header from the resulting corner.
With just three minutes left on the clock, United’s Slovakian stopper produced a wonderful stop to deny Salisu, who had peeled off at the far post and glanced Walker-Peters’ centre towards the bottom corner. But Dúbravka got down superbly to his right, clawing away the header before tipping an Armstrong drive over, leaving Newcastle to see out added time and secure the points with the kind of grit and discipline United fans have come to expect from Howe's charges during their recent revival.
