Two goals each from Chris Westwood and Adam Boyd put paid to the Conference side, but it wasn't as easy as the scoreline suggests.
Aldershot looked the better side for the remainder of the first half after they scored their 35th-minute consolation.
But it wasn't enough to produce a giant-killing.
Hartlepool didn't need long to settle, and Boyd sent a long-range shot over the bar as an early warning.
The striker's 25-yard effort was tipped round the post by Shots keeper Nikki Bull, and the home team took the lead from the corner with 12 minutes gone.
Gavin Strachan swung the ball in and defender Westwood was unmarked to head in from near the penalty spot.
He was in the same place on the half hour to grab the home team's second, stroking his shot home after the outstanding Joel Porter won possession on the right and crossed low from the goal line.
Between the goals, Pool had peppered the Aldershot goal. Tony Sweeney's brave header just off target, Boyd shooting straight at Bull and Westwood seeing another header cleared off the line in a combined effort by Bull and Darren Barnard.
But just when it seemed like plain sailing for the home team, Aldershot gave them a wake up call by narrowing the gap on 35 minutes.
Dwain Clarke crossed low from the left and Tim Sills was there to slide the ball in from close range.
Aldershot were on top for the rest of the half and again after the break, when Jon Challinor's long-range shot came back off the bar.
Pool recovered well, and two quickfire goals from Boyd won them the game.
On 62 minutes he headed Sweeney's cross into the top corner and then lashed his second into the roof of the net after great work from the outstanding Porter.
It was Porter who made the fifth on 75 minutes, heading down a cross for Mark Tinkler to pick his spot from 10 yards to rub salt in unfortunate Aldershot's wounds.