The former Kilmarnock player added a 27th-minute penalty before Nacho Novo made it three.
Boyd, who is out of contract at the end of the season, was linked with Fenerbahce and Newcastle in Saturday's papers but Gers boss Walter Smith fully expects him to be at Ibrox for the duration of his deal - and beyond.
"I get a wee bit fed up answering questions about this," Smith said.
"We have made it clear we don't have to sell anybody in this transfer window.
"I don't know where he's going, I read this morning he is going everywhere.
"We have not had anybody enquiring about him and hopefully we won't lose him until he decides to go, which could be two or three years down the road."
Smith praised Boyd's clinical nature in front of goal.
The manager added: "As we have seen over a number of seasons, it's no problem keeping him in the form of scoring goals - he scores goals all the time.
"He added to the total today and he's a little bit frustrated he didn't add to those two - goalscorers are a bit greedy.
"He has been terrific for us."
"We were pleased with the performance," Smith added.
"We obviously got off to a good start and throughout the match created an awful lot of opportunities.
"We should have done better when we did get the opportunities, and Graeme Smith made a couple of brilliant saves.
"But we seem to be creating a lot more chances over the last month than we did in the early part of the season."
While Smith was delighted with Boyd's continued form in front of goal, both goals were heavily assisted by St Johnstone's new-look central defence, leaving Saints boss Derek McInnes exasperated.
"Rangers thoroughly deserved their points but they didn't have to work hard for the goals," McInnes said.
"That's the galling thing. When you come to Ibrox you try to set up to frustrate them and get a foothold in the game and make it difficult.
"We did that at times but anytime they breached our midfield, defensively we never stood up to it.
"They were two of the poorest goals you'll see at this level and that's what cost us. The third goal wasn't much better."