City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat
The champions succumbed in the 72nd minute when Phillips latched on to a careless, under-hit back pass from Danny Drinkwater to outpace Wes Morgan and dink the ball expertly over Ron-Robert Zieler for his first Baggies' goal.
Three minutes later, Islam Slimani equalised from Riyad Mahrez's pinpoint cross -- the Algerian's first assist in his last 18 Premier League games -- but Leicester were left to rue another loss that leaves them just two points above the relegation zone.