The Norwich skipper struck twice in the first half to cancel out an equaliser from Damien Delaney, who was then sent off in the 37th minute for a professional foul on Holt.
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 npower Championship defeat for Ipswich but Norwich were more vibrant throughout as they moved back into the play-off zone.
The home side's manager Paul Lambert watched from the stands after being hit with a two-match touchline ban following last week's 3-3 draw with Reading, but his men did his talking for him with the football they produced.
They took the lead in the 13th minute when Ipswich defender Darren O'Dea dithered on the ball, allowing Holt to rob him of possession and fire a superb right-foot shot high past Marton Fulop.
Both sides passed up chances shortly afterwards before Ipswich 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.
In the 37th minute Delaney hauled down Holt as he threatened to race clear on goal and referee Keith Hill was left with no other option but to show Delaney a straight red card and leave Keane's men facing an uphill battle..
There were precious few second-half chances for either side until Holt grabbed his hat-trick goal in the 76th minute. Martin did superbly well to find him inside the penalty area and he drilled home a low right-foot shot.
Two minutes later, Hoolahan collected another fine pass from Martin and coolly chipped the ball over Fulop with his left foot.
Norwich: Ruddy, Russell Martin, Barnett, Ward, Lappin, Crofts, Surman (Hoolahan 64), Lansbury (Korey Smith 80), Fox, Holt (Jackson 85), Chris Martin. Subs Not Used: Rudd, Nelson, Johnson, McNamee.
Ipswich: Fulop, Zuiverloon (Fallon 69), Delaney, Smith, O'Dea, Edwards, Leadbitter, Norris, Colback, Scotland (Healy 42), Priskin (Brown 81). Subs not used: Murphy, O'Connor, Livermore, Civelli.