Hull overcame James Chester’s early red card to open the scoring on 42 minutes through Nikica Jelavic, but Stoke struck with seven minutes to go when Shawcross’ scruffy finished just sneaked over the line.
Chester, who scored last week’s winner at Queens Park Rangers and also conceded a penalty, was dismissed on 14 minutes for bringing down Glenn Whelan after Jake Livermore’s poor pass had put the defender in trouble.
The home side reorganised and took the lead three minutes before half-time when Asmir Begovic pushed out Tom Huddlestone’s low shot and Jelavic slid in to squeeze the ball home from a narrow angle.
Stoke toiled in search of an equaliser, with Charlie Adam testing Allan McGregor moments after coming on as a substitute, before Mark Hughes’ side levelled with seven minutes to go in fortunate fashion.
Phil Bardsley’s volley came back off the post, McGregor pushed the ball away and Shawcross’ close-range effort just rolled over the line via the Hull keeper and the upright, although referee Jon Moss took his time before awarding the goal.
Hull were left to fume with the goal coming from a Stoke throw-in which should have gone the home side's way.
Steve Bruce’s side were eager to assert themselves in the opening minutes, looking to get on the front foot and attempting to target Bardsley at right-back.
Andrew Robertson was the chosen outlet and he began to find his range with a couple of teasing crosses from the left.
Yet despite Hull's positive start, exemplified by the busy Stephen Quinn, Stoke were threatening on the break.
Their first warning came after only three minutes when Peter Odemwingie played in Mame Diouf, who shook off Chester to leave himself clean through but was judged to have fouled the defender in the process.
Chester was not so lucky next time, when Livermore's underhit back pass invited Whelan to charge at goal. All the momentum lay with the Irishman, who was left in a heap by an outstretched leg that had denied a clear scoring chance.
The tactical reshuffle was relatively simple, Ahmed Elmohamady and Robertson swapping wing-back to full-back and Tom Ince dropping deeper into midfield and it was a system Stoke struggled to pick holes in despite their advantage.
There were half-chances - an Odemwingie dribble into the area, Erik Pieters' wayward drive - but the hosts were holding up well.
Hughes responded by sending on summer signing Bojan Krkic four minutes before half-time, with Whelan sacrificed, but he was unimpressive in Hull's opener just seconds later.
Lacking the bite that Whelan would have offered, he allowed Huddlestone to breeze past him before unleashing a low shot that Begovic could only palm back out. Jelavic anticipated well, beat Marc Wilson to the ball and hooked home from a tight angle.
It was the least Hull's battling response deserved and it was the hosts who ended the half pressing for a second as Stoke lost all semblance of calm.
Hughes' half-time words seemed to have some effect, with his side much improved after the break.
McGregor was called on twice in as many minutes, saving low from Shawcross following a free-kick routine then diving in front of Diouf to smother a cross.
The respective managers quickly re-drew the battle lines, Hughes sending Peter Crouch on as a second striker and Bruce replacing Ince with another defender in Liam Rosenior.
Stoke had their best chance yet when Bojan's deft pass played in Crouch after 64 minutes but a clumsy touch allowed McShane to make a covering challenge. The ball looped invitingly for Diouf but his cushioned header landed a yard wide.
Stoke's final substitute, Adam, was into the game immediately, firing a 25-yarder that McGregor flicked over the crossbar.
The game was gradually building towards Stoke's response but Hull did not seem liable to crack.
It took a wrongly-awarded throw-in and an unusual bounce of the ball to breach them, Bardsley hitting Bojan's cross into the ground and watching it rear up and bounce off the frame of the goal.
McGregor, briefly disorientated, allowed it to come back off him instead of gathering it and Shawcross did just enough - his effort confirmed by goal-line technology.
There would no winner but Hull, ever game for the fight, ended the game bravely seeking one.