Wood’s 58th-minute header was enough to separate the sides in what was overall a poor contest at Turf Moor, giving Sean Dyche’s side their fifth Premier League win on home soil this season, all without conceding.
On a bitter Lancashire afternoon the first-half especially was found wanting for quality, and almost industry, given the majority of the opening 45 minutes was played at a relatively pedestrian pace.
From United boss Steve Bruce’s position it was a case of mend and make do, with his side shorn of four players who figured in last weekend’s 2-1 home win over Southampton through injury.
Without the pace of Allan Saint-Maximin and Miguel Almiron, in particular, Bruce handed Andy Carroll only his second start since a free move from West Ham in the summer, as well as the captain’s armband for the first time.
Unsurprisingly, when short of ideas, the ball was pumped forward for Carroll, which almost paid off in the fifth minute when Isaac Hayden’s cross picked out the towering forward for a header that flashed a couple of yards wide.
Burnley responded six minutes later when Ashley Barnes, one of three changes from the Clarets’ 5-0 hammering at Tottenham last weekend, played in Dwight McNeil for a stinging low shot from 22 yards that Martin Dubravka turned aside.
A contentious VAR call then arose in the 13th minute when Wood’s flick to a low ball in from McNeil caught the hand of Paul Dummett, who had slid in to challenge the striker, yet only a corner was given, much to the anger of the home faithful.
There was precious little action that followed, bar injury scares for Fabian Schar and James Tarkowski, the latter twice challenged by Joelinton in the space of two minutes, and earning a yellow card off referee Tim Robinson for his second studs-first tackle.
Mercifully, 13 minutes after the restart the deadlock was broken when Wood headed home an inswinging corner from Ashley Westwood at the far post, awarded after Federico Fernandez had rolled on the ball over the bye-line despite Bruce’s moans to the contrary.
A minute later Carroll’s captaincy debut was marred with a booking. Although always with his eyes on a high ball, his elbow in the face of Burnley captain Ben Mee drew the game’s second caution from Robinson.
Jack Cork should then have sealed the points in the 67th minute, but after stealing the ball off Sean Longstaff deep in United’s half and shrugging aside a challenge from Fernandez, his 10-yard shot was superbly saved by Dubravka.
Following a Joelinton 20-yard volley that caught the back end of the sidenetting, Wood then angled a left-wing McNeil cross into the near post narrowly over the bar.
Eight minutes from time Newcastle almost stole an equaliser, only for 71st-minute substitute Dwight Gayle to sidefoot wide from inside the six-yard box a low Joelinton cross from the left after he had contentiously barged Erik Pieters off the ball.