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In the day's other game, West Ham United stayed eighth after a fourth successive draw -- the last three of them goalless -- when they were held by managerless Swansea City, who are still in the bottom three.
The lacklustre defeat by Watford was a bad blow for Juergen Klopp's side, who would have overtaken them with a win but remained ninth, having taken only one point from three games.
Not since April 1987 have Watford, promoted to the top flight this season, won four successive games at this level of English football.
"It was an amazing victory against an amazing team," Quique Sanchez Flores, Watford's manager, told the BBC.
Yet the Spaniard was keen not to get too carried away with his side's progress. "We should be humble, we have a lot of matches to play," he added.
"Four wins back-to-back is massive and starts our so-called tough run that everyone's talking about," jubilant captain Troy Deeney added on Sky Sports.
"We're just doing our stuff and people have got to be worried to come here now."
Deeney and Ighalo have now scored 17 of the team's 21 goals between them this season. The captain, who plays just behind his team-mate, offered an insight into their understanding when describing the first goal.
"I was fighting for the ball but I know he's going to make a run. He makes it easy for me because he's so quick and strong."
"I know when he gets the ball, he will play it behind the defence," added Ighalo, which was just what happened.
The predictability of the move did not please Klopp, who criticised his team's "bad reaction" to conceding twice in the opening quarter of an hour.
He insisted the first goal should not have been allowed, however, claiming that goalkeeper Adam Bogdan, standing in for the injured Simon Mignolet, had both hands on the ball before Dutch full-back Nathan Ake knocked it over the line.
"I think it's a foul, it was a wrong decision, but our reaction was really bad," he said.
"We lost our mind and lost a very easy second goal, when we can defend better."
That one did not reflect well on centre-half Martin Skrtel, who seemed to have forced Ighalo wide from Deeney's pass but allowed him to score from a wide angle.
Skrtel limped off before halftime and Divock Origi came on hoping to make an impression as dramatic as last weekend's when his goal in the sixth minute of added time earned Liverpool a draw against West Bromwich Albion.
The Belgian's presence contributed to an improvement in the second half as the visitors finally made some chances, but Heurelho Gomes kept them at bay.
Ighalo's second goal in the 85th minute rounded off a fine move.
So Watford continue to confound critics who forecast a grim struggle against relegation following a return to the Premier League in May after an eight-year absence.
In 2006/07 they won only five games and finished bottom.
This eighth victory from 17 games leaves them handsomely placed although a tricky programme awaits over the festive period with games against Chelsea, Tottenham Hotspur and Manchester City.
West Ham, now three points adrift of Watford in eighth, came away with another 0-0 draw away to Swansea, who had 73 percent of possession but could not take their chances. The Welsh team remain 18th in the table on 15 points.
"I don't think we are a bottom three side," Swansea's interim manager Alan Curtis told the BBC. "In the quality of the last two performances, whoever does come in (as manager) will be confident they can lift us up the table."