Boyce scored the winner early in the second half after Livingston dominated the first period at the Tony Macaroni Arena. He was then substituted near the end.
Smith was taken off after only 16 minutes with a back spasm. “I think both will be all right,” said the Hearts manager Robbie Neilson. “Michael had a back spasm, we had it a couple of weeks ago with Craig Halkett. Playing Thursday night [at Celtic] and then on the astro at his age, it’s just a spasm we’d expect to settle down.
“Boycie was more a precaution. He had a wee calf problem previously and that’s why he couldn’t start on Thursday night. After 60 minutes he said he was starting to tighten up but he should be ok.
“I thought it was a game of four quarters. I thought we started well in the first ten minutes. We had a couple of half-chances but then the game became very scrappy. We had no control in the middle and they were picking up all the second balls.
“It was only when we brought Peter Haring on [after 29 minutes] that we got a bit of stability and that allowed us to grow into the game. You can't wait until half-time – sometimes you just need to do it. Thankfully it paid off.”
Following a triple first-half save from Craig Gordon, Neilson labelled his goalkeeper “world-class”. “I thought both goalkeepers today had some really good saves,” he said. “It was two teams that were trying to win the game, which was good to see, which at times means you are open at the back. Craig pulled off some top-class saves but that's par for him.
“Probably the biggest thing about him is his concentration levels. Because he's been at such a high level, there can be 20 minutes when he's not been doing anything and then he pulls off a world-class save. There are a lot of keepers who don't have that ability, but we're lucky to have him and hopefully he's here for a number of years.
Neilson is still hoping to contact the Scottish FA head of referees, Crawford Allan, over certain decisions taken by Bobby Madden in Thursday’s defeat at Celtic Park. Allan was on BBC Radio Scotland over the weekend discussing the game.
“It’s disappointing. I’m still trying to get hold of him. I don’t know why. I was told he was on annual leave until next Friday and that he hadn’t watched the game,” said Neilson.
“But then the next day he’s on the radio talking about it and explaining the reasons behind it.
“I make mistakes. Referees make mistakes. All you want is a reason for why things have been given. Then you can take that on board and feed it back to your players.
“That’s why you try to speak to referees. But if you are getting nothing back it’s difficult and then, if you have to listen to it in the media, it’s not great is it?
“I’m sure I’ll get a phone call at some point. This week? I won’t hold my breath.”