Marc Skinner's side took the lead twice in the first half through an unfortunate own goal and the energetic Emma Watson.
The Lasses showed great fight though to come back on each occasion with goals either side of half time, with Deanna Cooper scoring after a mazy solo effort before Amy Andrews struck early after the restart.
Man United then took advantage and ran into a 5-2 lead thanks to goals from Rachael Williams and Gabby George.
However, with five minutes added on in second-half stoppage time, there was time for Wales international Lois Joel to register her first goal for the club.
A strong Man United side looked to assert themselves on the game from kick-off, and they ended up carving open the first chance after just five minutes but Melvin Malard failed to get her header on target.
The hosts managed to edge themselves in front just three minutes when Hayley Ladd's corner wasn't cleared, and the last touch came off a United player before rolling over the line.
Man United looked set to double their lead seconds later via a quick counter-attack, but after being picked out by Geyse, Watson failed to convert due to a last-ditch Lia Cataldo block.
It was an all-action first-half with Becky Langley's side dragging themselves back level after a period of prolonged pressure. After picking the ball up in the home side’s half, Cooper drove into the box before coolly slotting into the bottom corner.
Both sides continued to push as the game approached the half-hour mark, but after some neat play on the edge of the area, Watson was slipped in by Maya Le Tissier and made no mistake this time by sliding it beyond the onrushing Claudia Moan.
The WSL side looked certain to extend their lead when Anna Sandberg's deflected cross was palmed away by Moan but only to the feet of Watson; however, the 18-year-old missed the target from a matter of yards.
With ten minutes left to play in the half, Geyse teased a rabona-cross into the box which Malard couldn't guide on target as Moan watched it drift wide.
Newcastle came flying out of the traps after the restart when Andrews made it two Women's League Cup goals in as many games with a tidy left-footed finish.
Katie Barker's first-time ball over the top was missed by George, allowing Andrews to twist and turn up against Millie Turner before curling a delightful effort beyond Safia Middleton-Patel.
After just over 20 minutes of both sides exchanging tame blows, Man United pushed ahead for the third time when Williams tapped home after United cleared an initial effort off the line.
Man United added a fourth six minutes from time through half-time substitute George, who was unmarked in the area and headed home a dangerous Sandberg free kick.
The Red Devils found the net for a fifth time when Terland found the back of the net from close range.
Newcastle refused to lie down, however, with Joel firing into the bottom corner from outside the box in added time.
Newcastle United Women: Claudia Moan, Lia Cataldo (Beth Lumsden 74), Deanna Cooper (Liv Watt 74), Hannah Greenwood, Demi Stokes, Emma Kelly (Lois Joel 55), Amber-Keegan Stobbs, Isabella Sibley, Jasmine McQuade (Kacie Elson 68), Katie Barker, Amy Andrews (Shania Hayles 74)
Subs not used: Grace Donnelly, Hannah Hawkins, Georgia Gibson, Ella Baker
