The pair scored within three minutes of one another after the break to continue the Gunners' unbeaten League Cup run at the Emirates Stadium after receiving a scare at the start of the second half.
The Gunners responded well to falling behind and, after seeing Ivan Klasnic come close to doubling the visitors' advantage, levelled through Arshavin as he fired across the face of goal.
Goalscorer turned provider three minutes later as the Russia international played in Park, who curled home a superb effort to ensure Arsenal would make the quarter-finals for the ninth successive year.
The north Londoners had to withstand a barrage of Bolton pressure to hold out for victory but the majority of the 56,628 crowd could celebrate fourth round success, as well as the return of Thomas Vermaelen from a two-month injury lay-off.
Both sides made a plethora of changes for the game but the Trotters side contained more experience than their north London counterparts.
The teams struggled to find any rhythm during the opening exchanges but Bolton regular Darren Pratley managed to eke out the first chance of note, breaking free through the middle and forcing Lukasz Fabianski to palm over from 20 yards.
Park tried a similar attempt at the other end, before the Trotters returned the attack and on-loan Gael Kakuta tested Fabianski with a low drive.
After a brief pause for Ivan Klasnic to receive treatment on his right shoulder, Yossi Benayoun got the home fans on their feet by turning Gretar Steinsson before curling a shot across the face of the goal.
The on-loan Chelsea midfielder's shot ended some distance wide and the home side's best chance of the period came from an unlikely source as Arshavin's free-kick teed up Vermaelen, who hit a fizzing strike that Adam Bogdan did well to save.
The Bolton goalkeeper was forced into action once again shortly afterwards as a low effort from Park threatened to sneak in the bottom right-hand corner.
The visitors looked rejuvenated after the break and took less than two minutes to break the deadlock.
Muamba won the ball off the dallying Frimpong and pressed forward, playing a neat one-two with Martin Petrov before rifling into the roof of the net.
Buoyed by the former Arsenal midfielder's goal, Bolton pressed forward and would have doubled their tally immediately afterwards if Klasnic had not applied so much pressure on Kakuta's right-wing cross.
But rather than collapse under the visitors' pressure, Arsenal pushed forward and levelled six minutes after falling behind.
The Russia international was again involved moments later when another dangerous run down the middle freed Park, who opened his body and curled a right-footed shot akin to that of Thierry Henry in his prime.
The home side's attacking impetus soon slowed after the former Monaco man's 56th minute goal as the Gunners were forced to defend, with Vermaelen's last-ditch challenge stopping Klasnic getting a close-range shot away.
Kakuta was the next to test the home side's rearguard with a free-kick, before Fabianski almost fumbled a speculative effort from substitute Chris Eagles.
The Arsenal goalkeeper soon redeemed himself as the Trotters continued to press, producing superb saves to stop Klasnic and then Cahill.
In between the two efforts Frimpong limped off and was replaced by Oguzhan Ozyakup, who was forced to help defend as Klasnic again took fire.
Fortunately for Arsenal the Croatian's shot flew over and the home side managed to hold out for victory, despite efforts from Cahill and Steinsson in stoppage time.