Twice Vicky Jepson’s side had the lead in their opening group game, but the Blades refused to give up and claimed a stoppage time winner.
Jepson handed first starts of the season to Jemma Purfield, Rinsola Babajide and Ashley Hodson and there was also the welcome sight of the returning Wales international Rhiannon Roberts.
Sheffield United included former Liverpool FC Women club captain Leandra Little and ex Reds stopper Becky Flaherty.
The Reds opened the scoring just past the half hour mark when Ashley Hodson found the net on her first start of the season.
Melissa Lawley cut inside and after her effort was blocked Hodson pounced to net from close range.