Watch Gilbert's press conference
It was the 30-year-old's second appearance in the Betfred.com World Championship in Sheffield and he showed calm belying his limited experience to pick up the biggest win of his career thus far (Phil Haigh writes).
Tamworth's Gilbert dropped off the tour at the end of last season and made it back at the third and final attempt at Q School. He won four matches to qualify for the Crucible and is through to the last 16 of snooker's biggest tournament.
Gilbert led 6-3 after Saturday's session and he edged the first frame of the day to extend his lead. Both men struggled to find any fluency and the next four frames were shared to leave world number 68 Gilbert on the brink of victory at 9-5.
Gould, who had reached the second round here in each of the last two years, showed tremendous fighting spirit and began to produce his best snooker of the match as he knocked in back to back centuries of 136 and 109 followed by a 55 to get back within one frame at 9-8.
But Gilbert remained calm and pounced on the best chance he had to win the game as he compiled what turned out to be a match winning break of 54 in the 18th frame. Gould battled for the snooker he needed but when Gilbert fluked the last red the match was over.
"It's a massive relief, at 9-5 I just wanted the match over as quickly as possible and Martin just started to play brilliantly," said Gilbert after reaching the last 16 of a ranking event for the second time in his career.
"I think at 9-8 he was favourite the way he was playing. I made a good fifty in the last, I just want to apologise to Martin for giving it the big fist punch when I fluked that red, it was just a massive game for me.
"I felt fine yesterday, I had no great expectations I knew that if I played alright I could compete. I started well and just carried it on. It was a bit of a struggle today but it has to be expected, I'm not used to playing here but now I've got over the line I feel great."
Gilbert is now likely to play Neil Robertson, who is 7-2 up on Ken Doherty, and added: "I think I've got a chance against anybody, I know my record and results don't show that, but I think I can beat anybody. But I know I can also lose to anybody, whether that's in the first round of the qualifiers or here. I know I'm a massive underdog whoever I go up against, but it'll be great to play in the three sessions and I'll just try my best.
"If I had lost the last match at Q-School I would probably never have picked up a cue again, so to be in the last 16 at the Crucible now is such a turn-around.
"I've probably got one of the worst attitudes in the game, I don't practise. I haven't lived the lifestyle the top players do, I've done the wrong things at the wrong times. But the last 12 months since I got back on through Q-School I've tried to do things properly, I've practised, I've tried to have a better attitude to the game.
"I'm not going to be one of those players that can sit there all poker faced, I'm emotional. I try and keep it all in but I can't at times. I've got a great girlfriend and things are more settled at home. So win, lose or draw I go home and everything's alright."
Meanwhile, Stephen Maguire will take a 6-3 lead over Luca Brecel into their second session tomorrow (Matthew Thomas writes).
Brecel made history as the youngest player ever at Crucible, and after a nervous start the 17-year-old showed glimpses of his talent.
Maguire won two very untidy opening frames then a break of 54 put him into a 3-0 lead. Both players missed good chances in frame four before Brecel missed the yellow and accidentally knocked the blue in, and Maguire did enough to lead 4-0 at the mid-session interval.
Brecel made the most of his chance in the fifth frame making a confident 96 to take his first frame at the Crucible. The Belgian made a 63 in the next but Maguire fought back to clear up and lead 5-1.
Another scrappy frame again went to Maguire after misses from both players and it looked as if the Scot would have a commanding lead at the end of the session. However Brecel made his first Crucible century with a break of 116, and a 62 in frame nine means he trails 6-3.
Ball by ball scoring and results from tournaments