Hearts advanced to their fifth Scottish Cup quarterfinal in six seasons after defeating Championship bottom-side Hamilton Academical in the second half.
After scoring a 50-yard wonder goal the previous weekend, Stephen Humphrys capped off a strong week by scoring the game's first goal at PLZ Stadium.
After the top-flight visitors completely dominated the first half, John Rankin's young team fought back, but Cammy Devlin's second goal on the 79th minute put the game beyond their reach.
The quarter-final draw for Robbie Neilson's team will take place on Monday.
These games are always challenging. Because of this, the game was broadcast on television tonight. We've thankfully avoided doing that, Neilson told BBC Scotland.
We had the upper hand in the first half, but we played poorly and missed a few opportunities in the second. However, the most crucial factor is that we will be in the hat on Monday.
"We've been in finals in the past couple of years, but we lost on penalties and in overtime because we couldn't move on. Hopefully this year, with the knowledge we've gained, we can complete the process.
Rankin wanted to put pressure on Hearts ahead of the game despite his team's recent improvement in performance.
But from the first minute on, his defense was under constant pressure as the Premiership club peppered the home defense, which Hearts controlled with 79 percent of the ball.
The visitors missed a flurry of early chances. Humphrys missed three chances much more easily than he did with his halfway-line attempt against Dundee United last Saturday before scoring from a tight angle low at Ryan Fulton's near post.
Lewis Smith shot wide and Lucas De Bolle fired a close-range attempt straight at Zander Clark as Hamilton responded admirably for a team that had played 120 minutes in a victory over the SPFL Trust Trophy semifinal three days earlier.
However, Hearts scored the game's second goal when Devlin, a substitute, poked in from close range. This gave the big away crowd of 3,500 people hope that they would win the cup at Hampden in June.
Robert Snodgrass was named the game's MVP.
Shankland's absence is felt by Wasteful Hearts - analysis.
Neilson challenged his forwards to step up in the absence of the captain, Lawrence Shankland, who was suspended and was the team's leading scorer.
By scoring the opening goal, Humphrys partially met that goal, but the on-loan Wigan player occasionally wasted opportunities, and Josh Ginnelly found it difficult to get into the game.
If Shankland had been available, it's possible that the tie would have been over by halftime.
The way that Hearts briefly lost the initiative in the game may also be of concern to Neilson, but the depth of his team was once again demonstrated as his substitutes assisted in regaining control of the match.
As the bottom-placed team in the second division, Hamilton undoubtedly has more important matters to attend to right now, but if they continue to perform at this level, it is unlikely they will end the season there.
The loss ends a six-game unbeaten streak across all competitions, but Rankin must be incredibly proud of what his young team produced after the break.
We had to treat them with the respect they merit.
Manager of Hamilton Academical John Rankin on BBC Scotland: "I felt that in the first half, we were apathetic and didn't even put a glove on Hearts. I was extremely proud of them, though, for the second half. I believed we posed a serious threat.
"Confidence won't be damaged. The players had a challenging week but still managed to achieve two victories. And tonight, I was happy with how the second half played.
midfielder Robert Snodgrass of Hearts on BBC Scotland: They just finished 120 minutes of play and a successful result in the middle of the week, so it was important to treat them with respect.
"We had a lot of chances and really controlled the game in the first half, in my opinion, and we could have scored more.". But the guys played really well, maintaining a perfect record to advance to the next round.
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