Healy - Keeping Kenwyne the key staying up
The Trinidad and Tobago international claimed his ninth goal of an injury-interrupted season in the 2-0 win over Stoke City on Saturday which eased the Black Cats seven points clear of the relegation zone.
With 14 games still to play and the Wearsiders travelling to Arsenal and Liverpool in their next two, they know they are not yet safe.
However, Healy, who scored the second against the Potters after replacing 10-goal Djibril Cisse, knows just how important Jones' potency could be.
Sunderland came under intense pressure to sell the former Southampton frontman to Tottenham last month with former Roy Keane target Darren Bent being thrown into the mix.
However, they resisted and instead persuaded him to sign a new long-term deal.
Healy said: ''Both Kenwyne and Djibril are popping up with very important goals for us.
''The fact the club turned down a very big bid and the chance to bring a player of Darren Bent's quality here shows just how highly everyone rates Kenwyne. He did it again on Saturday, and these are goals that should hopefully end up keeping this club in the Premier League. You can't put a value on that.
''We are not a one-man team, but the determination of Sunderland to keep hold of their best players shows how ambitious the club is to not just be survivors at this level, but really make a mark.''
If Jones' 77th-minute header finally eased the tension at the Stadium of Light after Stoke substitute Danny Pugh had enjoyed an astonishing escape when he handled Steed Malbranque's first-half header on the line, it was Healy's first league strike for the club which secured the points in injury time.
The 29-year-old Northern Ireland international has had to be patient during his time in the north-east - that goal was only his third in 10 appearances for the Black Cats since his arrival from Fulham.
However, it was hugely important as it helped ease Ricky Sbragia's side into 11th place and leave them within touching distance of the top half of the table.
But with the situation below them as tight as ever, he knows only too well that situation could change rapidly if they do not keep the points total ticking over.
Healy told the Sunderland Echo: ''We were pleased to see the league table and that we are up to 11th, but we are by no means safe.
''We have to keep grinding out results and believe we can go away and take something from the top five or six clubs.''
Sunderland are not in action this weekend having slipped out of the FA Cup after a 2-1 fourth round replay defeat at Blackburn Rovers last Wednesday night in which Healy also scored.
They resume in the league on February 21 with a trip to the Emirates Stadium, where they will hope they can put a further dent in Arsenal's hopes of remaining among the exclusive top-four club.