West Brom, to their credit, also kept probing forward but they lacked the class required to really open United up at the back.
Mourinho attempted to end the stalemate – and the tedium – by introducing Anthony Martial with half an hour remaining and his introduction undoubtedly lifted the quiet Old Trafford atmosphere.
Increasingly poor conditions and a general lack of thrust continued to inhibit both sides, but United did force Foster into wonderfully save on 66 minutes when he tipped a Lukaku effort around the post.
However, the plucky visitors then sensationally seized their chance when Chris Brunt delivered a corner from the right with 17 minutes remaining. Nemanja Matic panicked at the delivery and headed back inside to Rodriguez, who could not miss from three yards out.
United, sensing the impact of the result, threw everything forward but West Brom displayed some new-found defensive fortitude and held on for a famous victory.
United will want to forget the result and its significance as quickly as they can.
However, the fans of West Brom — and certainly Manchester City — are likely to remember it for quite some time.