The 19-year-old former Barcelona trainee drilled in a fine first-half strike as Wenger's faith in youth was once again justified.
Bendtner, himself only 21 but now a regular in the side, produced a powerful finish after 50 minutes to put Arsenal into the last eight after Emiliano Insua had equalised.
As expected, Arsene Wenger had shaken things up in the team selection for his 750th game at the helm, naming an entirely different starting XI from the one which let a 2-0 lead slip during the closing stages at West Ham in the EPL on Sunday.
There was, though, a more experienced look to this Gunners team, with veteran Mickael Silvestre captaining the side at the ripe old age of 32, while French midfielder Samir Nasri made his first appearance of the season after recovering from a fractured leg, while Croatia striker Eduardo was also in the team.
The hosts started well, and Merida - who almost went out on loan to Levante, only for Wenger to pull the plug on the deal at the last minute - fired a low effort just off target.
Only Dirk Kuyt, the Reds captain for the night, remained from the Liverpool side which had defeated Manchester United - although there was a welcome place on the bench for Alberto Aquilani, who had yet to play following his big-money summer move from Roma.
Liverpool created a decent opening when a clever backheel from David Ngog, on target at Anfield to help sink United, released Philipp Degen on the edge of the penalty area, but the Swiss defender dragged his shot across the face of goal.
On 10 minutes, Nasri was upended by Martin Skrtel just outside the Liverpool box, but chipped his free-kick over the wall and wide.
Bendtner then overcomplicated a one-two with Nasri, trying to stab the ball square to Aaron Ramsey, rather than just shoot when clear through.
Merida showed him just how it should be done with a fine strike on 19 minutes.
Craig Eastmond, 18, stole possession on the right, and the ball broke for Merida, who promptly smashed a first-time, left-foot shot in off the post past Diego Cavalieri.
Arsenal, though, had their lead only until the 26th minute when Insua netted a fine equaliser.
A long ball up field was knocked down by Ryan Babel, and it dropped perfectly for Insua, who drilled a looping shot up over Lukasz Fabianski from 25 yards for the Argentinian defender's first goal in English football.
Arsenal were soon back on the offensive, with Eduardo and Ramsey combining to set Merida clear on the left side of the penalty area, and the youngster did well to stay on his feet as Cavalieri charged out of goal.
There was another let-off for Liverpool when Cavalieri dropped the ball in a crowded six-yard box, but enough black shirts were around to clear.
Arsenal kept up their momentum following the restart, and went ahead again five minutes into the second period.
A sweeping move saw Merida feed the ball through to Bendtner on the penalty spot.
The Denmark international held off Skrtel before smashing his shot into the roof of the net.
To their credit, Liverpool came back strongly.
Fabianski had to get down to save a low, 25-yard free-kick from Babel which would have crept inside the keeper's right-hand post.
With 17 minutes left, Wenger made a change when 20-year-old Mark Randall and Hackney-born striker Sanchez Watt, 18, replaced