The Gunners showed no sign of a Carling Cup hangover as Orient were brushed aside in clinical fashion.
Marouane Chamakh set Arsene Wenger's men on their way in the seventh minute with his first goal since the end of November, before Bendtner's well-taken double put the result beyond doubt ahead of the interval.
The Denmark striker completed his treble from the penalty spot, with full-back Gael Clichy netting a rare effort with 15 minutes left.
Only Tomas Rosicky, who later limped off, remained from the starting XI left crestfallen at Wembley. Teenage defender Ignasi Miquel made his first home appearance and 19-year-old winger Connor Henderson a senior debut.
Centre-back Laurent Koscielny was, officially at least, rested because of a minor hamstring problem, while goalkeeper Wojciech Szczesny - the other guilty party in Sunday's costly mix-up - was on the bench.
Samir Nasri, Jack Wilshere and Andrey Arshavin were also among the substitutes should they be needed to help get the job done at the second time of asking.
The replay - earned after Orient forced a last-minute equaliser at Brisbane Road 10 days ago - was expected to bring in around £700,000 for the League One side, who are set for a trip to Las Vegas on chairman Barry Hearn at the end of a season which could yet finish with promotion via the play-offs.
The Os were cheered on by some 9,000 fans, most having travelled more in hope than genuine expectation of a cup shock which would be off the scale compared to Sunday's result at Wembley.
Chamakh was deployed in Robin van Persie's role at the spearhead of the attack, with the Dutchman set to be out for around a month with a knee injury picked up in scoring the equaliser against Birmingham.
The Moroccan settled any early nerves when he put Arsenal ahead from close range.
Rosicky darted into the right side of the Orient box before cutting the ball back to the penalty spot, where Chamakh guided a shot into the bottom left corner to take his tally to 12.
Orient almost produced a response when Ben Chorley, a former Arsenal trainee, sent an angled volley goalwards from a corner which was deflected over.
The away fans behind the far Clock End thought Alex Revell had steered in an equaliser from Charlie Daniels' cross, but the ball only rippled the side-netting.
Arsenal were soon back on the offensive and doubled their lead on the half-hour when Bendtner sent Kieran Gibbs' cross back into the top-left corner with a looping header from 12 yards.
It was 3-0 in the 43rd minute when Bendtner cut in from the left and curled a low strike into the far corner, for his sixth goal of the season.
Abou Diaby should have made it four at the start of the second half when he waltzed through the Orient defence, but dragged his low shot wide.
Orient refused to lay down and caused more than one moment of panic in the hosts' six-yard box.
However, Arsenal were then awarded a penalty on 61 minutes when Gibbs was tripped by Revell.
During the break in play, Rosicky, who had picked up an injury, was replaced by Nasri. Bendtner smashed the spot-kick into the bottom-left corner to complete his hat-trick, a second for Arsenal.
Wilshere and Clichy were given run-outs for the final 24 minutes, replacing Bendtner and Diaby.
The French full-back drilled number five into the bottom corner for his first goal since November 2008 as Arsenal booked a mouth-watering clash against their Premier League title rivals at Old Trafford on March 12.