Potter scored twice in the opening quarter of the game and Charlie Clare added a third as Tigers led 21-7 at half-time.
At the beginning of the Bank Holiday weekend, both head coaches named extended squads and used the second period to spread gametime through their ranks with the new Gallagher Premiership season now just two weeks away.
Anthony Watson, Jimmy Gopperth and James Cronin were among the Tigers newcomers to sample running out at their new home stadium, with Tom Horton, Joe Taufute’e and Phil Cokanasiga joining the action after the break.
Potter completed his hat-trick at the start of the second half, with Taufete’e and Sean Jansen adding further scores in the final run-put before the start of the new season.
After Newcastle kicked off towards the Beehive Money Stand, they enjoyed some decent possession but could not progress further than the 22 with Tigers tackling quickly until eventually turning over ball and, just moments later, Steve Borthwick’s men were on the scoresheet.
Potter recovered from an early tumble when he was impeded in collecting a high ball which led to a yellow card for Vereimi Qorowale to get the first points on the board after five minutes, taking a long pass on the left wing and then winning the race to his chip kick to dot down. Freddie Burns added the conversion for a 7-0 lead.
A knock-on from the restart gave Falcons put-in ball just 10 metres out from the Tigers tryline but the set-piece brought a penalty which Burns kicked back up to halfway.
Potter led the kickchase to a diagonal prod from Burns to the left-hand corner and was rewarded with a penalty but, when play was spread to the opposite flank, Chris Ashton was bundled into touch just five metres out.
Matt Scott showed pace and composure as he covered a dangerous kick down the Falcons right and then dodged two tacklers to allow Tigers to re-set and clear.
Potter was back on the scoresheet on 21 minutes as he collected a crosskick on the left just seconds after a second yellow card had been shown to Qorowale as he tackled Ashton close to the line on the opposite wing.
Falcons lost attacking scrum possession and then missed a lineout in the corner but, when Eli Snyman stole a lineout at the opposite end, a chip from Ben Youngs over last man Logovi’i Mulipola somehow slipped from Ashton’s reach.
George Martin showed strength and good footwork to lead the next attack, but Tigers lost ball 15 metres out and Falcons were able to clear the danger.
The home defence was tested with a break by Gary Graham up the middle and, when Falcons retained ball, it was the back-rower who broke a final tackle to score next to the posts. The conversion from Brett Connon made it 14-7 on 35 minutes.
But Martin’s lineout catch set up position for a third Tigers try shortly before half-time, with Falcons backtracking quickly as Clare touched down and Burns added a third conversion for a 21-7 lead.
England Under-20s cap Jed Walsh was added to the Tigers backline for the start of the second period, while Falcons changed their entire line-up in their first outing of pre-season.
The opening points came with a hat-trick score for Potter in the left-hand corner after some crisp work in attack and Burns added the conversion from the touchline as Tigers sent on five replacements from the bench including Taufete’e.
Falcons responded with a try from Iwan Stephens, winning the chase to ball on the left, with new fly-half Josh Thomas adding the extras as Borthwick sent on replacements including summer signing Cokanasiga.
When wing Adam Radwan was met with a double tackle on the tryline, Tigers continued to defend strongly until Falcons were held up in possession.
But straight from the drop-out, Falcons returned at pace, with Stephens releasing Radwan to score on the right and Thomas was on target with the extras to make it 28-21 with 10 minutes still to play.
A break from Cokansiga was appreciated by the sizeable crowd and ended with a fifth try, with Taufete’e forcing his way over to the left of the posts and Gopperth added the conversion.
But Falcons soon celebrated another try of their own, scrum-half Cameron Nordli-Kelemeti wriggling out of contact to run clear. Thomas added the extras to put just seven points between the teams entering the closing couple of minutes.
Horton replaced Taufete’e in the middle of the front row and was immediately on the ball on the left but Falcons stood up to the lineout drive.
They were pinned inside their own 22, though, and the game ended with Sean Jansen making the final push from a lineout drive for another Tigers try, which Gopperth converted from the right touchline.