Nigeria international Ighalo, who has now scored 20 goals in 24 league games in 2015, beat Tim Krul at the near post for the 26-year-old's first early on.
The striker then took Troy Deeney's pass to round Krul before the break.
Daryl Janmaat gave Newcastle a lifeline from close range but Steve McClaren's side struggled to create chances despite moving off the bottom.
The Magpies overtook fellow strugglers Sunderland after their 2-0 defeat by Bournemouth, representing one of the few positives on another miserable day for home supporters at St James' Park.
They have seen their team win only three of 25 Premier League games in 2015 and despite a second-half improvement led almost single-handedly by Dutch right-back Janmaat, they have only scored three goals in six league games this season.
Their depressing form matches last term when Newcastle were winless in their first seven league games before winning five in succession under former boss Alan Pardew.
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Former England boss McClaren said before the match that trying to turn around the fortunes of Newcastle, who narrowly missed out on relegation last season, was "a little bit like a car crash".
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And his side looked bereft of drive in the first half where Watford broke quickly and had the finishing touch required in the form of the impressive Ighalo.
Newcastle repeatedly attacked down the wings, but with only four of 40 crosses finding their target, and Papiss Cisse being withdrawn at half-time after missing one decent chance, there was a lack of cutting edge.
Florian Thauvin was the most lively of Newcastle's attackers but it took Janmaat's intervention to get them back into the game, the full-back finishing well after a one-two with Moussa Sissoko.
Boos rang out from some home supporters at the end of the game, and with Chelsea and Manchester City up next, McClaren's task is not about to get any easier.
Ighalo provided the composure in front of goal that Newcastle were lacking as he extended a fabulous scoring run that has made him the most prolific striker in England's top four divisions this year.
However, he was indebted to Watford skipper Troy Deeney, who was tireless in his support play and set up the second goal with a clever ball in behind the Newcastle defence.
Three of Ighalo's four Premier League goals this season have been assisted by his strike partner.
Deeney was not alone in putting in an impressive shift for the visitors.
Once Watford had established their lead they defended superbly as Newcastle threatened from the flanks.
A solid display by the Hornets' back four was aided by convincing performances from defensive midfielders Etienne Capoue and Ben Watson, who made his first Premier League start of the season.
Watford boss Quique Sanchez Flores was beaming at full-time, and with good cause after a performance in which his players always seemed to offer support to team-mates, whether in attack or defence.
Newcastle boss Steve McClaren: "I am trying to change a lot and being here two-and-a-half months, it is very difficult to change things around quickly. I think Newcastle have won three games in the last 25, after a good run in November last year, so there is history there that needs changing and turning around."
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Watford boss Quique Sanchez Flores: "We deserved it because we played really well. We have a very positive mentality and we always think we can win games.
"I am really pleased we have so much confidence. We are building a new team but we are playing as if we have played together for a long time."
Match ends, Newcastle United 1, Watford 2.
Second Half ends, Newcastle United 1, Watford 2.
Offside, Newcastle United. Tim Krul tries a through ball, but Daryl Janmaat is caught offside.
Attempt missed. Nyom (Watford) left footed shot from the centre of the box is high and wide to the left. Assisted by Steven Berghuis.
Jack Colback (Newcastle United) is shown the yellow card for a bad foul.
Foul by Jack Colback (Newcastle United).
Odion Ighalo (Watford) wins a free kick in the defensive half.
Substitution, Newcastle United. Gabriel Obertan replaces Florian Thauvin because of an injury.
Substitution, Watford. Adlène Guédioura replaces Ben Watson.
Delay over. They are ready to continue.
Delay in match Daryl Janmaat (Newcastle United) because of an injury.
Jack Colback (Newcastle United) wins a free kick in the defensive half.
Foul by Odion Ighalo (Watford).
Foul by Florian Thauvin (Newcastle United).
Nathan Aké (Watford) wins a free kick in the defensive half.
Etienne Capoue (Watford) is shown the yellow card for a bad foul.
Georginio Wijnaldum (Newcastle United) wins a free kick in the defensive half.
Foul by Etienne Capoue (Watford).
Substitution, Newcastle United. Rolando Aarons replaces Massadio Haidara.
Substitution, Watford. Nathan Aké replaces Jurado.
Foul by Moussa Sissoko (Newcastle United).
Jurado (Watford) wins a free kick on the left wing.
Attempt saved. Siem de Jong (Newcastle United) right footed shot from the centre of the box is saved in the bottom left corner. Assisted by Georginio Wijnaldum.
Offside, Newcastle United. Daryl Janmaat tries a through ball, but Moussa Sissoko is caught offside.
Substitution, Watford. Steven Berghuis replaces Almen Abdi.
Attempt missed. Florian Thauvin (Newcastle United) left footed shot from outside the box misses to the right. Assisted by Georginio Wijnaldum.
Attempt blocked. Troy Deeney (Watford) right footed shot from outside the box is blocked. Assisted by Sebastian Prödl.
Florian Thauvin (Newcastle United) wins a free kick in the defensive half.
Foul by Etienne Capoue (Watford).
Foul by Ayoze Pérez (Newcastle United).
Craig Cathcart (Watford) wins a free kick in the defensive half.
Attempt missed. Siem de Jong (Newcastle United) header from the centre of the box misses to the left. Assisted by Daryl Janmaat with a cross.
Attempt missed. Massadio Haidara (Newcastle United) right footed shot from outside the box is high and wide to the left following a corner.
Corner,  Newcastle United. Conceded by Heurelho Gomes.
Attempt saved. Daryl Janmaat (Newcastle United) left footed shot from outside the box is saved in the top right corner. Assisted by Florian Thauvin.
Corner,  Newcastle United. Conceded by Ikechi Anya.
Attempt missed. Troy Deeney (Watford) header from a difficult angle on the left is high and wide to the left. Assisted by Almen Abdi with a cross following a corner.
Corner,  Watford. Conceded by Chancel Mbemba.
Georginio Wijnaldum (Newcastle United) wins a free kick in the defensive half.
Foul by Ben Watson (Watford).
Newcastle's winless start to the season continued as Odion Ighalo's double led Watford to a second successive victory.