By Anthony Marshall - Newcastle United Journalist
Wolverhampton Wanderers 1 (Fletcher 88)
Newcastle United 2 (Ba 17, Gutierrez 38)
The victory also extended their unbeaten start to the season in all competitions to nine games, and gave the Magpies their first win at Molineux since April 1990.
Ba's close range header broke the deadlock for the Magpies, before a superb individual effort from Gutierrez doubled their advantage with half-time approaching. Steven Fletcher responded with time ticking away at the end of the match, but it was too little, too late for Wolves.
Despite the result, Alan Pardew's side did not have it all their own way. Goalkeeper Tim Krul made at least four outstanding stops to keep the hosts at bay, while Wolves will feel they should have had a penalty after Jamie O'Hara was felled inside the box, with a free-kick being given instead.
But United had that killer instinct in the final third and went away from the Midlands with all three points.
With just two minutes on the clock Krul was called into action to make a superb save. Ryan Taylor's foul on Fletcher gave the hosts a free-kick wide on the right, and O'Hara's inswinging delivery missed everyone's head and looked to be sneaking in the far corner until the intervention of Krul's fingertips.
Kevin Doyle scuffed an effort off target as Wolves dominated the opening exchanges, but Newcastle's pace on the break was always going to cause problems, and that proved to be the case on 14 minutes.
As United won possession deep in their own half, the ball was swiftly moved up to Ba, whose back-heel set Yohan Cabaye into space. The French international freed Gutierrez on the left, but his low curling effort fell the wrong side of the far upright.
And the Magpies took the lead on 17 minutes through the simplest of goals. Cabaye chipped a corner to the near post and Ba was given a free run to nod home his fourth goal of the season.
Wolves should have been level within three minutes but some heroic goalkeeping and defending kept the visitors' lead in tact. Doyle struck a left-footed shot which got a big deflection off Steven Taylor and looked to have wrong-footed Krul, but the Dutch stopper managed to get his legs in the way to block.
And as the loose ball fell kindly to Matt Jarvis about eight yards out for a relatively straightforward finish, he was thwarted by Ryan Taylor's last-ditch tackle.
Centre-back Christophe Berra hooked over from a corner as Wolves continued to press for an equaliser, but Newcastle were creating the better chances and in the 29th minute home keeper Wayne Hennessey was forced to dive full-length to his right to parry away Cheik Tiote's 20-yard drive.
Gutierrez should have doubled the lead almost immediately when Leon Best's low cross from the right found him completely unmarked at the front post, but Hennessey made a point-blank stop with his legs to deny the winger.
However, the Argentine was not to be denied for long and finally made it 2-0 on 38 minutes. As he and Cheik Tiote exchanged passes out on the left touchline it looked like there was nothing on.
But Gutierrez proceeded to waltz past tackles from Stearman and Roger Johnson before planting a low strike across Hennessey and into the far corner.
The Magpies had a lucky escape just before the break when Steven Taylor brought down Jamie O'Hara, with referee Mark Halsey giving Wolves a free-kick just outside the box. However, television replays showed the contact happened inside the area, and the visitors were given a let-off.
Just as they had in the first, Wolves started the second half brightly. A free-kick from O'Hara was not too far away from finding a gold head in the middle of the area, while Magpies defender Danny Simpson was forced to head a cross behind under pressure from Steven Hunt.
At the other end, Gutierrez tried to add to his - and Newcastle's tally - but his low shot from 25 yards lacked the accuracy or power to test Hennessey.
Wolves boss Mick McCarthy made a double change in the 58th minute, introducing Adam Hammill and Adlene Guedioura to try and increase his side's creativity, and within seconds Hammill's cross found its way to O'Hara on the edge of the box, but the midfielder skewed wide.
Fletcher volleyed high over the top from a good position as the hosts began to pose a threat again, with Hammill looking particularly dangerous, and one mazy run from the winger was only ended by a Steven Taylor tackle seven yards out.
How Wolves didn't find the back of the net on 66 minutes, only Krul knows. The keeper once again excelled, blocking Fletcher's close-range strike and getting up quickly enough to parry Doyle's follow-up to safety. It was a rare defensive lapse from United which had gifted the home side the opening, but Krul came to the rescue.
Johnson flashed a low effort across a crowded goalmouth as the visitors failed to clear yet another O'Hara set piece, but thankfully for those in black and white, a final touch was absent.
As time ticked away O'Hara had another chance to give Wolves a glimmer of hope but his half-volley from the edge of the area was brilliantly blocked by the body of Steven Taylor.
The hosts finally got the goal their efforts deserved in the 88th minute when Hammill's cross from the left was met by Fletcher at the far post to finally beat Krul with a firm downward header
Doyle thought he had snatched a dramatic draw when he stabbed home from close range deep into five minutes of stoppage time, but the linesman had signalled that the cross which reached him had gone out of play, and Newcastle held on for maximum points.
Wolverhampton Wanderers (4-4-2): Wayne Hennessey; Richard Stearman, Christophe Berra, Roger Johnson, Stephen Ward; Matt Jarvis, Karl Henry (Adam Hammill 58), Jamie O'Hara, Stephen Hunt (Adlene Guedioura 58); Steven Fletcher, Kevin Doyle
Subs not used: Dorus De Vries, Matt Doherty, Ronald Zubar, Dave Edwards, Sam Vokes
Newcastle United (4-4-2): Tim Krul; Danny Simpson, Steven Taylor, Fabricio Coloccini (c), Ryan Taylor; Gabriel Obertan (Sylvain Marveaux 90), Yohan Cabaye (Danny Guthrie 89), Cheik Tiote, Jonas Gutierrez; Leon Best, Demba Ba (Peter Lovenkrands 71)
Subs not used: Rob Elliot, Davide Santon, Sammy Ameobi, Hatem Ben Arfa
Referee: Mark Halsey