Those strikes sandwiched a Liam Boyce penalty in the first half in what was a dominant performance from the hosts.
Australian Devlin also became an instant hit with the home fans on his full debut with a lively display in the middle of the park.
Neilson said: "Barrie's performance was the reason we brought him here.
"Cammy's another piece in the jigsaw; he's 23, he's got energy, pace, mobility and he can deal with the ball.
"I was really pleased with the way we played. We've been like that in the majority of games we've played this season.
"Today was a day that the majority of things we've been working on came to fruition.
"Livingston have had tough games – Sunday, Wednesday, Saturday, against Celtic, Rangers and Hearts.
"So we knew it would be important to bring energy that would allow us to dominate the game. I think we've a decent squad here now. All in all, it's been a good day."
Livingston manager Davie Martindale admitted the game had been a step too far for his team after facing Old Firm sides twice within seven days.
The Lions could not recreate the heroics that saw them beat Celtic last Sunday.
Martindale said: "It was a tough one, I'm not going to sit here and tell lies.
"I think you could see that the last two games have caught up on us. I'm not using that as an excuse but I think it played a big part in how we approached the game.
"We were very passive and quite lethargic and we gave away possession too easily.
"I don't think it comes down to attitude, I think we were lethargic and we were quite passive out of possession, which isn't a Livingston performance.
"We didn't get a chance to put pressure on the ball in the mid-third, which gave Hearts too much time on the ball and they kept moving us. You're running about and chasing shadows."