But Ipswich, in contrast, now seem comfortably clear of relegation trouble.
There was no sign for most of the first half that Hull would slump to their tenth home defeat of the season and their biggest defeat so far at the KC Stadium.
With veteran Dean Windass providing plenty of class and Nicky Forster's non-stop running, Hull looked the more likely winners.
They were rewarded for incessant pressure midway through the half when Stuart Elliott headed Sam Ricketts' cross against the bar for Windass to prod the rebound home.
But Ipswich quickly equalised as Hull centre-back Damien Delaney failed to cover a long ball out of defence and was then completely perplexed by the close control of Jeffers, who slid his shot beneath Boaz Myhill.
It was the start of what became a nightmare for Delaney and his centre-back partner Danny Coles.
Just before half-time Gary Roberts took advantage of Coles' inability to clear and slid a square pass to the other side of the area where Jaime Peters' shot took a deflection off Ricketts and left Myhill stranded.
Hull returned to attack and Windass volleyed just over the top.
It turned out to be their last real chance of reward as Ipswich dominated the second half with Alan Lee soon scoring the third, racing 40 yards after Jeffers found him with a through ball.
Just after the hour Coles tried to head a free-kick from Owen Garvan back to Myhill but placed the ball wide of the goalkeeper, gifting Jason De Vos the simplest of openings.
Myhill then made an amazing one-handed save to deny Garvan.
Hull desperately tried to claw their way back from an impossible position and were repeatedly caught on the break by Ipswich's speedy raiders.
Sub Danny Haynes sped away to hammer the fifth before Windass casually converted a penalty awarded against Garvan.
Ipswich outplayed Hull in midfield during the one-sided second half with Garvan and Sylvain Legwinski always prominent.