Stephen Hunt bagged his second goal in three games to clinch three massive points for Wanderers.
Blues had two half-chances to level during a late surge of pressure, with one falling to unmarked Phillips who could only mis-direct a difficult header off target from 10 yards.
Phillips admitted: "It was very unlike a Birmingham display, we battle and play a lot better than that. It was a bad day at the office.
"Credit to Wolves, they were up against it with the injuries they`ve got. They were a lot better."