Dani Ceballos' injury-time strike saw Arsenal squeeze past Sheffield United 2-1 in their FA Cup quarter-final clash at Bramall Lane on Sunday.
Nicolas Pepe's first-half penalty appeared to have sent the visitors to Wembley - the forward's eighth goal of the season - only for David McGoldrick to stab home an equaliser with just three minutes left to play.
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However, with extra time seemingly beckoning, Ceballos found himself in the right place to finish off an Arsenal counterattack with a neatly taken goal that keeps his side's season alive as they progressed to the semi-finals of the competition for a record-equalling 30th time.
Sheff Utd: Henderson (6), Basham (6), Egan (6), Robinson (8), Baldockn (6), Stevens (6), Fleck (6), Lundstram (7), Norwood (6), McBurnie (7), McGoldrick (8)
Subs: Freeman (6), Berge (6), Sharp (7)
Arsenal: Martinez (8), Tierney (9), Mustafi (8), Luiz (6), Maitland-Niles (7), Willock (6), Kolasinac (6), Xhaka (8), Lacazette (6), Pepe (7), Saka (6)
Subs: Sokratis (6), Holding (6), Ceballos (7), Nketiah (6)
Man of the match: Kieran Tierney
The Blades, though, have still to win since they returned to action three games ago and must now concentrate on trying to secure a place in Europe next season via their Premier League placing.
How Gunners made it to another FA Cup semi-final
Ninety-eight days after the two teams were originally due to meet in the last eight of the FA Cup, they finally did in a tie of huge significance for both clubs.
Despite not having their usual vociferous home support to drive them on, the Blades still began on the front foot against opponents with David Luiz back after his recent suspension, but with top scorer Pierre-Emerick Aubameyang only a substitute.
Chris Wilder and his players thought they had gone ahead after just nine minutes when John Lundstram nodded home Oli McBurnie's own header back across the six-yard box following a left-wing corner.
However, the Video Assistant Referee was on hand to correctly deem the defender offside and so it was Arsenal who actually went in ahead at half-time thanks to Pepe's calmly dispatched penalty correctly awarded after Chris Basham caught Alexandre Lacazette in the box.
It was a different Blades team in the second period, though, no doubt driven on by some stern words from their manager, who watched another 'goal' by John Egan ruled out for offside after McGoldrick had just gone too early at a free-kick.
The Blades made three changes from Wednesday's 3-0 loss at Man Utd, with Dean Henderson back in goal, while John Egan and Oli McBurnie also returned.
Arsenal made five changes to the team that won 2-0 at Southampton in the Premier League on Thursday with Ainsley Maitland-Niles, David Luiz, Joe Willock, Sead Kolasinac and Alexandre Lacazette recalled in place of Hector Bellerin, Rob Holding, Dani Ceballos, Pierre-Emerick Aubameyang and Eddie Nketiah. However, Mesut Ozil missed out with a back injury.
The hosts kept pushing, however, and got their rewards when some slapstick Arsenal defending saw Sead Kolasinac's late clearance hit Rob Holding and fall straight at McGoldrick's feet, and the forward could not miss.
But if Sheffield United thought they had done enough to force extra time, they were wrong as Arsenal launched one last break up field that ended with Ceballos jinking his way into the area and somehow sliding a low shot past Henderson at his near post for his first goal for the club.
- Sheffield United have lost three matches in a row in all competitions for only the second time since Chris Wilder's appointment in 2016, also doing so in December 2017
- Arsenal have now won seven of their last 10 matches in all competitions (L3), as many as they managed across the previous 27 matches beforehand (W7 D14 L6)
- Sheffield United have fallen at the quarter-final stage of the FA Cup for the first time since 2004 and the 11th time overall - the exact same number of eliminations as arch-rivals Sheffield Wednesday have endured at this stage
- Arsenal's opener - Nicolas Pepe's penalty - was the Gunners' first FA Cup goal from the spot since current boss Mikel Arteta netted against Everton in a 2013-14 quarter-final tie - a campaign in which they went on to win the competition
- Both of David McGoldrick's two goals for Sheffield United in all competitions this season have been scored in the FA Cup (from four shots); however, the forward is yet to score in 23 Premier League appearances having attempted 37 shots in that competition this season
Man of the Match - Kieran Tierney
It is fair to say the left back has endured a stop-start nature to his Arsenal career after his big-money move from Celtic last summer, interrupted first by a double hernia he underwent before arriving at the Emirates and then after suffering a dislocated shoulder against West Ham last October.
However, since returning to the starting XI, the Scotland international has shown just why the Gunners were so keen to bring him south of the border and his display against the Blades was further proof of his eye-catching abilities.
The 23-year-old was rock solid in the visitors' five-man back line, as well as providing a constant attacking outlet down the left with his surging runs, and was unlucky not to create a second first-half goal for Pepe after another such foray.
And what is more, it was his pass that led to the foul on Lacazette for Arsenal's crucial opening penalty that sent them on their way to victory.
What the managers said
Chris Wilder: "I had complete belief we would get back into the game. I thought we dominated the game in the second half and missed the best chances, and I thought we would have another chance to win it. A couple of boys are just a bit short of belief but there are certainly encouraging signs from our point of view."
Mikel Arteta: "I am really pleased. It is a really tough place to come and we got the result we wanted. We fought right until the end and I really liked the attitude of the team.
"They are really good at what they do. They put you under pressure all the time with their direct play. They put you in trouble. We dealt with that really well but you know at some stage you are going to suffer. We did but the reaction straight away was really good."
The Blades are back in Premier League action when they face Tottenham at Bramall Lane on Thursday, a match you can see live on Sky Sports.
Live Premier League
Arsenal, meanwhile, take on struggling Norwich on Wednesday, with both games kicking off at 6pm.