Hearts defeated Championship bottom-side Hamilton Academical in the second half to advance to their fifth Scottish Cup quarterfinal in six seasons.
Stephen Humphrys capped off a strong week for himself by scoring the game's first goal at PLZ Stadium to follow up his 50-yard wonder goal from the weekend.
After the top-flight guests completely dominated the first half, John Rankin's young team fought back, but the game was lost to them when Cammy Devlin stabbed in a second on the 79th minute.
In Monday's quarterfinal draw, Robbie Neilson's team will learn who their opponents will be in the last eight.
These games are never easy. In an effort to catch a mistake, that is why the game was broadcast on TV tonight. Thank goodness, we were able to avoid doing that," Neilson told BBC Scotland.
"In the first half, we were in charge, but in the second, we played poorly and missed a few opportunities. The fact that we will be in the hat on Monday is what matters most.
We've been in finals in the past couple of years, but we were unable to advance because we lost on penalties and in overtime. With the knowledge we've gained, hopefully we can complete the process this year. ".
Despite his team's recent improvement in form, Rankin was eager to put pressure on Hearts in the days leading up to the match.
But as the Premiership club peppered the home defense in the first half, which Hearts had 79 percent of, the pressure was immediately transferred back to his defense.
Humphrys missed three chances much more easily than his halfway-line attempt against Dundee United last Saturday before scoring from a tight angle low at Ryan Fulton's near post as the away team missed a flurry of early chances.
Hamilton responded well for a team that had played 120 minutes in a victory over the SPFL Trust Trophy semifinal three days earlier, with Lewis Smith slicing wide and Lucas De Bolle rolling a close-range attempt straight at Zander Clark.
However, Hearts scored the game's second goal when substitute Devlin poked in from close range, sending the 3,500-strong away crowd back along the M8 daydreaming of cup victory at Hampden in June.
Robert Snodgrass won the game's MVP award.
Analysis: Wasteful Hearts miss Shankland's presence.
Lawrence Shankland, the team's leading scorer, was suspended, so Neilson challenged his forwards to fill in for the captain.
Humphrys partially achieved this by scoring the game's opening goal, but the on-loan Wigan player was occasionally wasteful and Josh Ginnelly found it difficult to participate.
If Shankland had been available, the tie might have been over by the time the halftime bell rang.
Neilson may be concerned about the way in which Hearts briefly lost the initiative in the match, but his squad's strength was once again demonstrated as his substitutes assisted in regaining control of the match.
Although Hamilton is currently at the bottom of the second tier and has more important things to focus on, it is unlikely that they will end the season there if they continue to perform at this level.
A six-game unbeaten streak in all competitions comes to an end with the loss, but Rankin can be extremely proud of what his young team produced after the break.
Reaction: "We had to treat them with the respect they deserve.".
John Rankin, the manager of Hamilton Academical, spoke to BBC Scotland. "I thought we were apathetic in the first half and didn't put a glove on Hearts. But I was really proud of them after the second half. I considered us to be a serious threat.
"The confidence won't be shaken. Despite having a difficult week, the players managed to get two victories. And tonight's performance in the second half pleased me. ".
Robert Snodgrass, a midfielder for Hearts, spoke to BBC Scotland. It was important to treat them with the respect they merit since they had just completed 120 minutes of play and a successful result in the previous week.
"I felt like we really controlled the first half of the game and had plenty of chances to score more. But the guys played really well, keeping the scoreless, and moving on to the next round.
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