The 39-year-old was a surprise January signing by Eagles manager Ian Holloway and a surprise inclusion in the starting line-up, having previously made six substitute appearances since his move from Blackpool.
But he marked his first start in style with a treble to take his tally for the club to five as Palace moved to within a point of Steve Bruce's Hull, who dropped to third.
Jay Simpson pulled one back for the Tigers but Wilfried Zaha hit number four before David Meyler struck again in stoppage time.
Phillips may not have been given the chance to open the scoring from the penalty spot had Glenn Murray not missed from 12 yards earlier in the first half.
The former England striker had wanted to take that spot-kick, so when referee Mark Haywood controversially awarded Palace a second penalty, there was only going to be one outcome.
Hull keeper David Stockdale denied Murray, the country's top scorer, a 29th goal of the season but he could not keep out Phillips.
Six minutes after the interval Phillips grabbed his second when he collected a pass from Zaha and, despite hitting his shot into the ground, it had enough power to beat Stockdale.
And 60 seconds later he completed his hat-trick with a deflected effort from another clever pass from Zaha.