Diomansy Kamara slid in the opener for the Baggies, before Chris Perry put through his own net to make it 1-1.
Phillips grabbed his second from Zoltan Gera's cross before he set up Kamara to make it 4-1, and curled in a 20-yard shot with seconds left for his third.
West Brom caretaker manager Nigel Pearson:
"It's an irony of football. This has been coming because we know we have good players. Although I am delighted with the result, in a way it's a shame it came now.
"Once you get a label for being unable to win away it can cause a barrier. Ultimately it was probably the reason for the change of leadership, but that's football.
"This was undoubtedly the most clinical performance we have given all season."
Ipswich boss Jim Magilton:
"When we fell behind we did not seem to have the spirit to come back.
"West Brom had more desire than us They were a level above us and it was an eye-opener.
"We just didn't sense danger at all and we defended too deep. We must now lick our wounds and put it behind us."
Ipswich: Price, Bruce, De Vos, Naylor, Harding, Currie (Bowditch 54), Legwinski, Walton (Richards 79), Noble, Lee, Clarke.
Subs Not Used: Supple, Sito, Macken.
Booked: Walton, Naylor, Bruce, Noble.
Goals: Perry 36 og.
West Brom: Zuberbuhler, Albrechtsen, Perry, Curtis Davies, Robinson, Gera (Ellington 87), Carter, Koumas (Quashie 80), Greening, Kamara, Phillips.
Subs Not Used: Steele, Hartson, Watson.
Booked: Greening, Koumas, Carter.
Goals: Kamara 29, Phillips 40, 54, Kamara 56, Phillips 90.
Att: 22,581
Ref: K Woolmer (Northamptonshire).