Canaries skipper Holt struck twice in the first half to cancel out an equaliser from Tractor Boys defender Damien Delaney, who was sent off in the 37th minute for a professional foul on the striker.
Keane's men rarely threatened an equaliser in the second half and, after Holt completed his treble in the 76th minute, substitute Wes Hoolahan added a fourth two minutes later.
The result marked a fourth successive Championship defeat for Ipswich but Norwich were more vibrant throughout as they moved back into the play-off zone.
Canaries boss Paul Lambert was forced to watch from the stands after being hit with a two-match touchline ban following last week's 3-3 draw with Reading.
Lambert was at least allowed to speak to his players before the game and at half-time, although his men did his talking for him with the football they produced.
They led in the 13th minute when Ipswich defender Darren O'Dea dithered on the ball, allowing Holt to rob him of possession and bear down on goal before striking past Marton Fulop with a superb right-foot shot into the far corner.
Holt sank to his knees in celebration but Ipswich threatened an immediate riposte when Tamas Priskin escaped down the right flank and crossed low into the six-yard box.
Norwich goalkeeper John Ruddy palmed the ball away to safety and the hosts threatened again when on-loan Arsenal midfielder Henri Lansbury curled a left-foot shot over the crossbar.
Holt then drilled in a fierce low cross from the left flank and strike partner Chris Martin narrowly failed to connect.
Yet the visitors drew level in the 29th minute when Grant Leadbitter's deep free-kick was headed down by Priskin and pounced on by Delaney, who nodded in from point-blank range.
Parity lasted for just six minutes as Lansbury's delightful slide-rule pass cut the Ipswich defence apart and found Holt in space.
The powerful frontman controlled the ball and drilled a low right-foot shot into the net from 14 yards.
Keane's side was dealt another blow in the 37th minute when Delaney hauled down Holt as he threatened to race clear on goal.
Referee Keith Hill was left with no other option but to show Delaney a straight red card.
Keane replaced striker Jason Scotland with Colin Healy in the 42nd minute but Ipswich struggled to threaten Norwich's goal as the second half progressed.
There were precious few scoring opportunities for either side until Holt grabbed his hat-trick goal in the 76th minute.
Martin did superbly well to find Holt inside the penalty area and he drilled home a low right-foot shot.
Two minutes later, salt was rubbed in Ipswich's wounds when Hoolahan collected another fine pass from Martin and coolly chipped the ball over Fulop with a neat left-foot finish.