Boyd did grab his second of the day - and his seventh of the season - after the interval but a barrage of goals failed to materialise and Saints ensured a nervous finale when Stephen O'Donnell pulled a goal back with two minutes to go.
Rangers managed to hold on for the win which allowed them to move to within a point of SPL leaders Celtic ahead of their visit to Falkirk.
And, in a week where Smith's men earned a draw against Unirea Urziceni in the Champions League and several players - Kevin Thomson, Steven Smith and Kyle Lafferty - were struck down by sickness bug, the Rangers boss was pleased just to get the points on the board today.
He said: "When you go away for the European games and you have the Wednesday-Saturday games, you always have a problem, especially when we lost two or three players to a bug they picked up in Romania.
"So we were pleased to come back and win the game - that was an important factor for us, although it was a little bit closer at the end than we would have wanted.
"I always think St Mirren are a difficult team to play against and there were periods of the game where they imposed themselves and we had to work hard against them. But we were delighted to win the game in the end."
Teenagers Danny Wilson and John Fleck were once again in fine form after impressing in recent matches and both were singled out for praise by Smith.
"They did well again and have been doing well in the other games as well," he said. "It was nice to see Fleck involved in a couple of goals. That was good to see."
However, there was a blow when Steven Whittaker was forced out of the game at half-time and he is now expected to withdraw from the Scotland squad ahead of next week's friendly in Wales.
"He's got a hamstring injury," said Smith. "He had it in Bucharest and it was tightening up as the first half went on.
"I would think it's likely [he would pull out] but I don't know yet. I haven't managed to find out from the physios exactly what the situation is but I would imagine it would cause him to pull out."
There was also bad news for the under-21s, with Stephen McGinn unlikely to make the trip to Azerbaijan for their European Championships qualifier.
Saints boss Gus MacPherson said: "He has a problem with his back. We're not too sure what it is.
"He had been struggling a little bit in training and we don't know whether it has gone into a spasm or not.
"It was restricting his movement in the last ten minutes of the first half. We asked him if he could give it a go in the second half and quite clearly he couldn't.
"I don't think he will make the under-21s. He will have to see the Scottish medical team but he has no chance of playing."
The Buddies boss added: "It was the worst possible start we could have had but credit to them for the way they came back after that.
"You have to be brave to try to play in the manner in which we did in the first half. We tried to pass the ball and we created two or three opportunities.
"If we had scored the goal five minutes earlier, there may have been a real chance for us. But, by then, it was practically time up."