Jack Harrison scored a stunning 25-yard drive as Leeds United progressed into the FA Cup fifth round for the first time since 2016 at the expense of League One Accrington Stanley.
Harrison fired into the bottom-right corner after Patrick Bamford's lay-off to break the deadlock halfway through the first half.
Leeds continued to press in a lively first half that saw 18 shots, with Luis Sinisterra having a curling effort tipped on to the bar.
They got the second goal their excellent forward play deserved when Junior Firpo linked up brilliantly with Bamford, with the striker's dragged reverse pass allowing the left-back to slot home for his first ever Leeds goal.
Sinisterra then sealed Leeds' comfortable passage when he opened his body and guided home Harrison's cross with Bamford also ready to pounce.
Accrington started brightly and eventually got their consolation when 18-year-old substitute Leslie Adekoya scored his first senior goal with a clever dink over Illan Meslier, 38 seconds after coming off the bench.
Leeds have gone six Premier League games without victory but the FA Cup is providing solace and could add confidence that boosts their survival fight.
The first half was full of chances at both ends with only a brilliant block from Maximilian Wober denying Accrington's Shaun Whalley, before January signing Georginio Rutter dragged wide from the edge of the area for Leeds.
The moment of quality arrived through Harrison, whose effort was simply unstoppable.
Accrington had chances to equalise, with boyhood Leeds fan Harvey Rodgers dragging wide when unmarked at the back post in the opening stages of the second period.
Leeds pressed and Bamford's quality eventually told when he did superbly to hold up Firpo's pass and then turn and release the left-back.
The 29-year-old striker, who has one England cap, has only managed 581 minutes this season so far but a return to fitness and form will add undoubted quality to Leeds' relegation fight.
Marsch called the 75 minutes that Bamford played a "big step", adding: "We were both just really happy - he was exhausted. He hasn't had that feeling in quite some time. He will be important for us."
Harrison, who has also struggled to make an impact this season with the performances of Wilfried Gnonto seeing him start on the left wing, then showed more quality when his cut-back was perfectly weighted into the path of Sinisterra.
Accrington, who only booked their place in the fourth round with a replay win over non-league Boreham Wood on Tuesday, deserved their consolation goal and it was a moment that Adekoya will never forget, having previously made just seven appearances off the bench for the club.
At 18 years and 285 days, he became the youngest player to score in this season's FA Cup.