Hamilton boss John Rankin insisted he always had faith his Accies would come good in the end after surviving a cup scare from East of Scotland Premier League leaders Musselburgh Athletic.
An 89th minute goal from Sean McGinty and an Oli Shaw strike five minutes into stoppage time spared the Championship outfit from extra-time with the sixth tier side, after Burgh’s Jamie Todd had struck early in the second half to cancel out Stephen Hendrie’s 24th minute opener.
Plucky Burgh also missed a huge chance through Jordan Smith to level again before Shaw sealed it.
But Rankin insisted he felt their place in Monday’s fifth round draw was never in doubt.
He said: “I always felt it was coming. Sometimes you can get your fingers burned at the opposite end when you keep going like that, but I knew that we’d had a few late goals this season.
“Oli always seems to pop up at the end. It wasn’t a great day for him but we always leave him on because you know he’s worth a goal.
“I said to the players that it didn’t matter how we got there, as long as we did and we’ve done that.
“Coming off the pitch a few of them were joking they’d rather have a Premiership team in the next round because it won’t be as hard as it was today.”
It took 20 minutes for Accies to create the first real opening of the game and they should have taken it. Connor Smith swung in a corner from the right, finding McGinty unmarked in the centre of the box, but he powered a header wide of the target from 10 yards when he had the goal at his mercy.
Five minutes later, the hosts took the lead in style. Smith clipped his corner kick to the left edge of the box and Stephen Hendrie rifled home an unstoppable strike into the bottom corner to give them lift off in the tie.
Musselburgh were a whisker away from an equaliser on the half hour mark when Robert Wilson’s drive on the edge of the box took a deflection and whizzed just past Charlie Albinson’s post, with the keeper rooted to the spot.
At the start of the second half though Burgh were level. Nathan Evans launched a long throw into the Hamilton box and nobody was picking up Jamie Todd, who stooped to angle a header into the bottom corner and send the travelling support wild.
Accies almost restored their lead in 59 minutes when Reghan Tumilty got on the end of Jamie Barjonas’ corner, scooping a shot narrowly wide.
Connor Smith went down in the box under pressure in 74 minutes but referee Graham Grainger wasn’t interested as Accies desperately searched for a winner.
Nine minutes from time Oli Shaw had a glorious chance when he latched on to Steven Bradley’s long ball and fired straight at Burgh keeper Liam McCathie inside the box.
Shaw struck the crossbar with a looping header in 88 minutes from a Hendrie cross as the visitors clung on for extra-time.
But Burgh hearts were broken in 89 minutes when McGinty got on the end of Smith’s corner to hammer home.
In stoppage time Jordan Smith spurned a glorious chance for a late leveller when he skewed wide from close range.
As Burgh pushed for a leveller and threw goalkeeper Liam MmCathie up for a late corner, Accies cleared upfield and Oli Shaw was able to nip in and net a clincher in the 95th minute.
Rankin is relieved to be in the hat for the next round but was left disappointed his side weren’t able to keep a clean sheet.
He added: “The message at half-time was don’t give them any encouragement and that’s what we did with the goal. You could see they got their backs up, they got excited and we gave them energy, which is really disappointing on our part.
“I’m really disappointed we didn’t keep the clean sheet and I didn’t think we were positive enough in the final third.
“We get a wee bit of quality from Connor for McGinty’s goal and Oli seals it, but the last one could have went either way. Everybody is up, the goalkeeper is up and if somebody switches off it could have gone to extra-time.
“It is a credit to the players that they kept going.”