United are coming into this cup clash after a six-goal thriller with Harrogate United last week, whereas Stoke were denied any points against Preston North End after conceding a last-minute header.
Match preview
Hartlepool are finding their second-straight season in the fourth tier of English football quite challenging and are struggling to progress after a comfortable 17th-placed finish last campaign.
Keith Curle's men are currently 22nd in the League Two standings having collected just 19 points from 24 matches, a tally which has them three points clear of Rochdale, who occupy one of the two relegation places.
Conceding too many goals has been the main issue in County Durham since the season kicked off in the summer, with United allowing 45 strikes past their goalkeeper in 24 games - nine more than any other team in the division.
The FA Cup has been a welcome distraction so far this term, with a penalty-shootout win over National League's Solihull Moors and a 3-1 success over Harrogate in November securing the club's berth in the third round for only the second time in six years.
Although the team has been faltering overall, striker Josh Umerah - who signed from non-league Wealdstone United in the summer - has excelled in his new role of Football League marksmen, scoring eight times in 21 starts following on from a 16-goal season in the fifth tier last season.
Stoke are one of a host of Championship clubs that have struggled since returning from the World Cup break, with Alex Neil's men managing just one win in five second-tier fixtures following the unprecedented break in club football.
The Potters looked set for a respectable point against Ryan Lowe's Preston on Monday afternoon until an in-form Ched Evans glanced Alan Browne's set-piece delivery beyond Jack Bonham in the Stoke goal.
That 93rd-minute winner sent the Lilywhites supporters into raptures at the bet365 Stadium and prompted the home faithful to begin a mass exit of the ground, with their side now hovering just four points above the relegation zone.
A cup clash against lower-league opposition will provide an opportunity for Stoke to build some momentum after a difficult festive period, although they should not underestimate a Hartlepool side who will be desperate to be in the fourth round draw.
Stoke's best ever FA Cup result was during the 2010-11 season, when they reached the final before losing 1-0 to Roberto Mancini's Manchester City - any repeat of such a run will make up for what looks set to be an uninspiring finish in the Championship.
Hartlepool United FA Cup form:
D
W
W
Hartlepool United form (all competitions):
W
L
W
W
L
D
Stoke City form (all competitions):
W
D
W
D
L
L
Team News
Hartlepool announced the signing of Matty Dolan this week from Newport County, but the defender is cup-tied, so he will not be able to feature against the Potters on Sunday.
Euan Murray is a doubt for this FA Cup clash, with the 28-year-old suffering from illness over the past week, an absence which would significantly weakened the United backline.
Stoke remain without midfielder Sam Clucas for the trip to County Durham, with the 32-year-old still suffering from a back issue sustained last month - although the ex-Swansea City man has not featured since October.
Neil confirmed in his pre-match press conference that Dwight Gayle has trained this week and will be involved in the matchday squad on Sunday, whereas Dujon Sterling is still a couple of weeks away from a return to action.
Hartlepool United possible starting lineup:
Killip; Shelton, Menayese, Ferguson, Tumilty; Cooke, Featherstone, Sylla; Grey, Umerah, Hamilton
Stoke City possible starting lineup:
Nonham; Wilmot, Souttar, Fox; Clarke, Thompson, Baker, Tymon; Smallbone; Campbell, Brown
We say: Hartlepool United 0-2 Stoke City
Hartlepool have nothing to lose as they head into this tough assignment against Championship opposition - something that will make a pleasant change from a League Two campaign clouded with relegation worries.