After a slow start, the hosts took the lead through Caolan Lavery’s impressive finish and an Adam Jackson own-goal soon lifted the home support further.
Gareth Evans then slotted in another after the interval and Marc McNulty added a fourth late on to stretch the Blues’ unbeaten run to seven matches.
Paul Cook made two changes from the side that progressed to the third round of the FA Cup by beating Accrington the previous week.
Lavery – who had been ineligible to feature against Stanley – replaced Adam McGurk, while Matt Clarke made way for Christian Burgess.
Former Pompey keeper Trevor Carson received a warm round of applause when he took up position in the Fratton End goal for Hartlepool.
The game was slow to get going, with the strong winds making passing football difficult for both sides.
Ben Davies swung in an early corner that none of his team-mates were able to make a connection with.
Then, after Adam Webster was dispossessed in the centre, Brian Murphy had to get down to hold Rakish Bingham’s shot.
And Bingham soon took advantage of heavy touch from Christian Burgess, but was unable to find the target.
There were nothing more than half-chances to warm up the crowd, with McNulty drawing a comfortable save from Carson and Davies fizzing a free-kick past the post.
Kyle Bennett livened things up on 32 minutes, however, with a fierce 20-yard effort that flew narrowly wide.
And the Fratton faithful were buoyant moments later, when LAVERY broke the deadlock with a fine strike from the edge of the box that flew into the top corner.
The visitors then gifted Pompey a second goal on 37 minutes, as Jackson was only able to divert Davies’ low cross into his own net.
Matthew Bates almost copied his central defensive partner and would have breathed a sigh of relief when his mis-cued header flew safely into Carson’s arms.
Murphy had enjoyed a quiet afternoon at the other end, but was called into action just before the break with a diving save to keep out Scott Fenwick’s sweetly-struck volley.
Hartlepool United 0
Evans should have extended the hosts’ advantage early in the second half, but fired wide after McNulty had embarked on a mazy run to tee him up.
They received a let-off at the other end, though, when Enda Stevens conceded a free-kick that Jake Carroll curled narrowly wide.
A corner then led to an almighty scramble in the Blues box before Evans eventually got the ball to safety.
And EVANS soon made up for his earlier miss by scoring Pompey’s third goal just past the hour mark.
Stevens did well down the left and fed McNulty, who showed quick feet to beat a couple of challenges and get a shot away.
His effort was well saved at point-blank range by Carson, but Evans popped up to confidently tuck away the loose ball.
Cook made his first switch on 75 minutes, with Bennett making way to allow Ben Tollitt a run-out, while McGurk came on for Lavery soon after.
It took a fine last-gasp challenge in the box from Stevens to prevent Nicky Featherstone from reducing the deficit.
Pools substitute Mikael Mandron was then booked for a late challenge on Christian Burgess, which saw the defender limp off and be replaced by Clarke.
The closing stages passed by without much incident, but McNULTY added a fourth goal at the death, calmly slotting home after being sent through by Stevens.
It meant there was plenty of cheer when the final whistle was blown, with the hosts delivering a festive feast.
Pompey (4-2-3-1): Murphy; Davies, Burgess (Clarke 85), Webster, Stevens; Hollands, Doyle (c); Evans, McNulty, Bennett (Tollitt 75); Lavery (McGurk 80)
Goals: Lavery 33, Jackson 37 (og), Evans 61, McNulty 90
Subs not used: Bass, Haunstrup, Close, Chaplin
Hartlepool (4-3-2-1): Carson; Duckworth, Bates, Jackson, Carroll; Gray, Featherstone, Magnay (c) (Walker 75); Oates, Fenwick (Mandron 75); Bingham
Booked: Bingham, Mandron
Subs not used: Bartlett, Harrison, Woods, Richards, Smith
Referee: Christopher Sarginson
Attendance: 15,610 (145 away fans)