Liam Boyce’s 50th-minute strike settled the match at the Tony Macaroni Arena, but it was Gordon’s heroics in the first half that kept the Jambos in it as Livingston threatened to run away with the first half.
In the same minute, Gordon made a point-blank stop from Andrew Shinnie, before turning a Jason Holt effort on to the post and then blocking Allan Forrest’s shot.
Gordon then made a strong save from Forrest in the second half as Hearts held on for a precious win that puts them five points clear in third place in the cinch Premiership.
"I thought both goalkeepers had some really good saves,” said Neilson. “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.
Neilson went on to quip “It's down to the coaching!” before adding: “He's just a top keeper. 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.”
The Hearts boss was forced to change his tactics and personnel midway through the first half due to Livingston’s superiority, switching to a 4-2-3-1 and replacing Ben Woodburn with Peter Haring. “You can't wait until half time – sometimes you just need to do it,” said Neilson. “Thankfully it paid off.”
Neilson did have to make two enforced changes, with right-back Michael Smith limping off early on and goalscorer Boyce replaced later in proceedings.
“I think both will be alright,” said Neilson. “Michael had a back spasm and we had it a couple of weeks ago with Halkett. Playing Thursday night and then on the astro at his age it’s just a spasm we’d expect to settle down.
“Boycey was more a precaution, he had a wee calf problem previously and that’s why he couldn’t start on Thursday night. After 60 mintes he said he was starting to tighten up. But he should be OK.”
On the match itself, Neilson added: "It was a game of four quarters! I thought we started well in the first five, 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 in that we got a bit of stability and that allowed us to grow into the game.
"We had a couple of chances to put it to bed and didn't manage to do it, and at 1-0 it was a wee bit edgy towards the end of the game, but we defended well. Livingston are a tough team to play against, especially here. They can be very erratic and they compete well, Davie's got them hardened and they put the ball into difficult areas, so for us to see out a 1-0 was great."