The Dutchman netted United’s second goal in the 90th minute to settle the contest where the Baggies threatened an equaliser throughout the second half after Gareth Macauley’s early own goal.
However, van Persie’s impact of the bench proved decisive and Ferguson was delighted with him.
“Robin is a fantastic player. He came on and changed the game for us,” Ferguson said.
“Every time the ball went to him he got hold of it and he did really well for us.”
The United boss was also delighted with the performance of returning midfielder Shinji Kagawa who has been absent due to injury in recent months.
“Shinji did very well in the first half. Obviously you expect him to tire with it being his first game for a couple of months and at that point we brought Robin on,” Ferguson said.
“I’m very pleased with Shinji - he did his job very well and he worked very hard in the early parts of the game.”
United remain seven points clear at the top of the Premier League table.