Garry Monk's side earned a comfortable victory over the Potters on Saturday and remain on course to finish in the Premier League's top eight, which would be their best ever finish
The Ecuadorian stooped at the far post to head in a Jonjo Shelvey cross after 76 minutes, before substitute Ki Sung-yueng made sure of the points in stoppage time, pulling Swansea within four points of seventh-placed Southampton.
Both sides are looking to secure their best Premier League finish, having previously peaked at ninth, but the first half passed by with little incident – Steven N'Zonzi's late dipping effort, saved by Lukasz Fabianski, as close as either team came to opening the scoring.
The hosts stepped up their game in the second period and looked the most likely to go ahead, but Gylfi Sigurdsson squandered a glorious opportunity to put his side in front when he headed over from close range seven minutes into the second half.
Montero finally broke the deadlock with 14 minutes left to play, and Ki wrapped up Swansea's victory with a straightforward finish after Stoke had seen Marc Wilson sent off for a second bookable offence.
Goalkeeper Asmir Begovic - at fault for Sunderland's opener in a 1-1 draw at the Britannia Stadium last weekend - dropped out of Stoke's matchday squad, while Neil Taylor returned from suspension to feature at left-back for Swansea.
The home side had concerns for their own goalkeeper, Fabianski, in the opening minutes following a coming together with Stoke midfielder Charlie Adam - playing with a broken nose - and the Pole was almost caught in possession by Mame Biram Diouf moments later.
But chances were at a premium for both sides for much of a stop-start opening period, with Nelson Oliveira, who was later forced off with an ankle injury, firing into the side-netting from a Montero cross as one of few promising situations fizzled out.
Shelvey guided a tame 20-yard effort into the arms of Butland five minutes from the break, marking the game's first shot on target, and N'Zonzi had Fabianski sprawling before time was up with a dipping effort from just outside the box - the Swansea stopper touching over.
Sigurdsson rattled the crossbar with a terrific effort from just inside the penalty area shortly after the restart, before Diouf escaped a yellow card for an apparent dive in the penalty area, evoking memories of Victor Moses' tumble that controversially earned Stoke a spot-kick in the reverse fixture, which ended 2-1 in favour of Hughes' men.
Sigurdsson, unmarked, then headed over from six yards out, and Marko Arnautovic could maybe count himself lucky to avoid being sent off for catching Nathan Dyer with his studs showing as the match approached the hour mark.
Another chance for Swansea came and went as Sigurdsson saw an effort deflected wide from the centre of the box, but Montero eventually made the breakthrough.
Shelvey beat Erik Pieters out on the right, before Montero shrugged off Phil Bardsley to head home at the far post.
Things went from bad to worse for Stoke when Wilson was sent off for a second bookable offence, their first red card of the season, although Butland pulled off a superb save to deny Shelvey from the resulting free-kick.
Holes began to appear all over the pitch for Stoke as they chased an equaliser, and Ki was left with a tap-in from another Shelvey assist in stoppage time.