Van Persie's sixth United goal was enough to claim a barely deserved win in another bad-tempered encounter in which Jonjo Shelvey became the fifth player sent off in the last six league meetings between the two old rivals.
The United striker settled a incident-strewn game nine minutes from time after referee Mark Halsey controversially awarded a penalty after Glen Johnson's challenge on Antonio Valencia, enabling the visitors to climb into second place and leave Liverpool in the bottom three.
But Halsey's performance will have only increased the frustration for Brendan Rodgers, after the Liverpool manager lost Shelvey shortly before half-time after a lunge on Jonny Evans. The midfielder was involved in a fierce confrontation with Sir Alex Ferguson as he stormed off towards the tunnel.
Though Liverpool did take the lead through Steven Gerrard, Rafael restored parity before Van Persie produced the vital contribution to leave the hosts still waiting for their first league win under their new manager.