Phillips drew Albion level in the 88th minute, before pouncing in injury time to earn Albion their seventh successive home win.
The Baggies had done it the hard way as second-half strikes from Keith Keane and Warren Feeney had cancelled out Jason Koumas' opener.
Luton looked set to record their first away win since beating Barnsley at the end of September before Phillips' late one-two.
The defeat left Luton boss Mike Newell seething as Town's David Bell was injured when Phillips equalised and he felt that the game should have been stopped.
It was certainly rough on Luton who had more than held their own against high-flying Albion, but they were undone by the predatory instincts of Phillips who took his tally for the season to 11.
Phillips' persistence fired Albion level when he converted a cross from Paul Robinson before rising to head home a free-kick from Koumas.
But the win came at a cost as Albion's highly-rated central defender Curtis Davies suffered a first-half foot injury that could sentence him to a spell on the sidelines.
To add to Albion's growing selection problems, Koumas picked up his fifth booking of the season. He is now banned for next weekend's trip to Leeds United, along with striker John Hartson.
The defeat was rough on Luton. Had they been more clinical in the first half, when Feeney and Steve Robinson missed gilt-edged chances, they would have been in control before Koumas struck with his seventh goal in 12 games.
There appeared little danger when Koumas collected a pass from Phillips 40 yards from goal.
But he jinked his way past the challenge of Ahmet Brkovic and Keane and into the area before curling his shot beyond Dean Kiely.
It looked good enough to seal another home win for Albion only for them to be undone by Luton's battling qualities.
Keane stunned them on the hour when he exchanged passes with Robinson and drilled home his first goal of the season from 12 yards.
You could see the confidence drain from Albion and Town took full advantage after 70 minutes.
Bell fed Adam Boyd and his neat cross was calmly slotted home as Feeney grabbed his fourth goal of the season, good work that was undone by the late heroics of Phillips.