Phillips looked to have put Albion on the way to a win that would have moved them a point away from second-placed Stoke City with two games in hand when he broke the deadlock by reaching his double century with his 20th goal of the season in the 30th minute.
But Albion paid a high price for failing to build on that strike and Moses made them pay as the first goal of his fledgling career picked up a point for a Palace side, who deserved some kind of reward for an improved second-half display.
Potentially just as worrying as dropping two points for FA Cup semi-finalists Albion was the fact that key wingers Chris Brunt and James Morrison both limped off with ankle injuries.
Phillips, 34, had two early sighters before he earned himself a place among the few players to have reached 200 goals.
The former England international was just off target in the eighth minute after being sent clear by Zoltan Gera.
He was then inches wide with a close-range header following a left-wing cross from captain Jonathan Greening.
But he made it third time lucky on the half hour following a sweeping cross-field pass from Paul Robinson.
Phillips collected the ball on the edge of the area before chipping his shot over the advancing figure of goalkeeper Julian Speroni.
Despite the best efforts of the lively Moses, Palace failed to test Albion goalkeeper Dean Kiely in a generally low key first-half.
But they only needed 10 minutes of the second half to change all that when Albion's defence was caught napping.
Ben Watson and James Scowcroft combined well to set-up Moses, who found himself unmarked six yards out at the far post and with the simple task of stabbing the ball past Kiely.
Unfortunately for Moses, he had little chance to bask in his goalscoring glory as he limped off six minutes later following a heavy challenge.
Palace lost some of their attacking momentum with his departure and Albion almost took advantage only for Speroni to produce smart saves from Ishmael Miller and Kim Do-Heon as Albion's search for a winner proved to be fruitless.