The Argentina international provided the flourish with a sublime injury-time strike as the Magpies defeated Wolves 4-1 at St James’ Park to calm frayed nerves after a run of just one win in nine league games.
That left them in ninth place on Saturday evening, seven points above the relegation zone with as many matches left to play and with a goal difference of plus two.
Newcastle, of course, were relegated two seasons ago on 34 points when just one more would have kept them up, although the total required this season is likely to be significantly higher.
But Gutierrez is convinced 42 will be enough for the promoted club to achieve its one and only aim for the campaign, and if that target is reached at Aston Villa next Sunday, all the better.
The 27-year-old said: “We need a few more points and the quicker we can get them, the better.
“I think three points will be enough to give us another year in the Premier League, and then we will see where we are and where we can go.’’
The Magpies approached Saturday’s game knowing there was little margin for error, but expecting the toughest of tests against a resurgent Wolves side which had taken eight points from the previous 12 on offer to give themselves real momentum in their own bid for safety.
However, for 50 minutes, the game was painfully one-sided as Alan Pardew’s men assumed complete control and threatened to win at a canter.
Skipper Kevin Nolan, who later picked up his 10th booking of the season and a two-match ban for a cynical trip on winger Adam Hammill, opened the scoring with a neat 22nd-minute finish, his 12th of the season, after running on to Shola Ameobi’s flick-on.
Ameobi helped himself to a second on the stroke of half-time when he powered home a header from Peter Lovenkrands’ inviting cross, and when the Dane steered Joey Barton’s pinpoint ball past goalkeeper Wayne Hennessey five minutes after the break, the visitors were in disarray.
However, Wolves belatedly found a rhythm and after striker Sylvan Ebanks-Blake converted Matt Jarvis’ 58th-minute cross, Newcastle briefly wobbled in the face of an onslaught.
But the storm abated as time ran down and Gutierrez had the last word when, after substitute Steven Taylor had made an important block inside his own penalty area and surged forward down the left, he played in the South American to cut inside and curl a delicious shot across Hennessey and into the bottom corner.
Wolves boss Mick McCarthy admitted his side had endured a bad day at the office as they slipped into 19th place, but promised they will be better when they entertain Everton next Saturday.
He said: “Does a team that’s been in the bottom three as long as we have suddenly become a great team that’s going to play well every week?
“Well no, it’s not, so we have had a bad one (today). But we will re-group (on Monday) and we will get ready for Everton, and we will be better.”