But the final scoreline was rough on Ipswich, who had dominated the second half before Albion's late three-goal blast.
The Baggies controlled the first half and should have been out of sight by the interval.
But Ipswich, who have not won at The Hawthorns since 1999, ran the second half and will be wondering how they headed back to Portman Road pointless.
Alan Lee had enough chances to have won the game for Ipswich on his own, but was out of luck in front of goal - particularly when he hit the post in the 65th minute.
It was a surprise that it took Albion as long as 23 minutes to break the deadlock.
Phillips twice went close in the opening six minutes before Ipswich produced their only threat of note in the opening period when Lee dragged his shot wide after good work by Pablo Counago.
But it was Albion that carried the greatest threat with Miller heading just wide before both Phillips and Teixeira were inches away from converting Chris Brunt's cross.
When the breakthrough came, it was due in no small part to Miller's sheer physical presence.
He raced on to a pass from Teixeira and forced his way past defenders Dan Harding and Alex Bruce before calmly pushing the ball beyond goalkeeper Neil Alexander with the outside of his left foot from six yards.
Miller could have helped himself to a hat-trick before half-time as he headed wide from close range and then failed to hit the target with a low drive.
It would have been hard for Ipswich to have been as poor again in the second half and they were a different proposition after a rocket from boss Jim Magilton.
Lee set the tone for an improved Ipswich display when he forced Dean Kiely to make a smart stop barely 60 seconds after the re-start.
Counago then fired across the face of goal and Lee was denied for a second time by Kiely.
Kiely, who had been a virtual spectator in the first half, was suddenly the busiest man on the pitch when he then frustrated Counago.
But he was relieved to see the post come to his rescue in the 65th minute when Lee met David Wright's cross only for his header to crash against the woodwork.
They were to prove to be costly misses as Albion gave the final scoreline a flattering look with their three late goals.
Teixeira collected a raking cross-field ball from Paul Robinson in the 87th minute and beat Alexander from the edge of the area.
He then turned provider for the unmarked Phillips who steered the ball home from four yards.
Phillips set the seal on the victory in stoppage time when he was picked out by Robinson and pounced from 20 yards.