The Blues’ final 3,000 seats were snapped up within two-and-a-half hours of going on general sale this morning.
Such was the demand, when the Frogmore Road ticket office opened at 10am queues stretched around the corner and into Carisbrooke Road.
Now they have all been taken, ensuring there will be a bumper crowd at Saturday’s fourth round tie.
Bournemouth today also announced their allocation of 2,800 have been bought by supporters.
Fratton Park’s current capacity is 18,931 and it appears that will be reached for the visit of Eddie Howe’s side.
Pompey’s biggest attendance this season was against Reading for the Capital One Cup in August, attracting 18,190.
Last weekend’s visit of Oxford United drew their largest League Two crowd so far this the season with 17,840 present.
However, the U’s failed to sell out their Milton end allocation, with 2,047 seats of the available 2,600 snapped up.
In the Cherries’ case, they have had no problems selling their tickets, irrespective of the 52 miles between the south coast clubs.
It means Pompey will be setting their highest home attendance since the Championship visit of neighbours Southampton in December 2011.
A crowd of 19,879 attended that 1-1 draw, with the capacity reduced in recent years for health and safety reasons.
Paul Cook’s side booked their place in the fourth round following last week’s 2-1 victory over Ipswich.
Gary Roberts and Marc McNulty both scored first-half goals in the Fratton Park replay, which attracted a crowd of 17,020.
Pompey also defeated Macclesfield and Accrington at home in previous rounds to enjoy their best FA Cup run since getting to the 2010 final at Wembley.
Bournemouth, who entered at the third round stage, previously defeated Birmingham City 2-1.
Glenn Murray’s 85th-minute goal sealed the victory after the Cherries had initially fallen behind.
However, it was a much-changed side fielded by Howe and he could again opt to rotate his squad for Saturday’s trip to Fratton Park.
Although that could mean a reunion for Sylvain Distin – who won the 2008 FA Cup with Pompey.