Newcastle had taken the lead with a lucky goal in the 25th, as Ryan Taylor's cross was headed toward goal by Yohan Cabaye and then deflected off Liverpool defender Daniel Agger to wrongfoot goalkeeper Pepe Reina.
But Bellamy equalized five minutes later with a low shot into the bottom left corner after a poor clearance fell right at his feet, and added the second with a free kick in the 67th.
Gerrard came on as a substitute for his second appearance after a two-month injury layoff and scored the third after running on to a ball from Jordan Henderson and slotting it underneath goalkeeper Tim Krul from a tight angle.