Phillips took his season tally to 15 with a second successive double and he should have helped himself to a hat-trick as he
saw his 58th minute spot-kick saved.
With Robert Koren, Zoltan Gera and Craig Beattie also on target Albion have now scored 13 goals in their last three home games.
This latest victory turned in free-scoring Albion's favour during a dramatic 10 minute spell at the end of the first-half.
Scunthorpe boss Nigel Adkins was sent to the stands by referee Neil Swarbrick for complaining that Phillips was
offside when he opened the scoring in the 35th minute.
Left-back Marcus Williams was then dismissed in the 43rd minute for bringing down Gera and two minutes
later Koren doubled Albion's lead with his second goal in two games.
Scunthorpe, whose win at Preston on Boxing Day had been their first in 12 games, were simply in damage limitation mode in the second half.
They were denied any kind of reward for their efforts by a smart double save by Dean Kiely in the 64th minute when he first pushed an Ian Morris header on to the bar and then tipped over the follow up from Jonathan Forte.
And the margin of Scunthorpe's defeat would have been greater but for the heroics of former Albion goalkeeper Joe Murphy.
He starred in the second-half, frustrating Ishmael Miller five times as well as denying Phillips from the spot.
But Murphy was unable to prevent the former England striker putting Albion further in control seven minutes into the second-half as Phillips finished a move that he started.
When Miller was brought down by Murphy six minutes later it was tailor-made for Phillips to complete his treble but his penalty was weakly hit and Murphy dived low to his left to turn away the shot.
There was nothing he could do in the 77th minute however as Gera collected a short pass from Chris Brunt and let fly with a dipping 20-yard drive.
And if Scunthorpe thought things could not get any worse they were wrong as Scottish international Beattie cut in from the left-hand edge of the area and beat Murphy for a fifth goal and a win that sends the Baggies clear at the top of the Championship table.