The 19-year-old midfielder crumpled in a heap after a foul by Ryan Shawcross, which earned the Stoke centre-back a straight red card in the 66th minute.
Ramsey was attended to on the pitch by medical staff for several minutes and needed oxygen before he was stretchered from the field.
The youngster received a standing ovation from both sets of supporters while the clearly upset Shawcross made the long walk with his head bowed.
Arsenal had leaked three goals from Rory Delap long throws in losing on their previous two visits to the Britannia Stadium, so it wasn't a massive surprise when the same weapon worked again in the eighth minute.
Delap's flat delivery from the right was headed on by the unmarked Shawcross and Danny Pugh was also unattended as he stooped to nod home at the far post.
Pulis had been concerned that his players would be tired after Wednesday's extra-time FA Cup victory over Manchester City, but there was no sign of that as Stoke's power-play dominated the opening exchanges.
Arsenal were struggling to make any dents in a rock-solid home defence, with Abdoulaye Faye and Shawcross marshalling operations superbly.
But Arsene Wenger's men gradually got their passing game together to exert some pressure and they equalised with an excellent goal in the 32nd minute.
Cesc Fabregas' cross from the right was immaculate and Nicklas Bendtner rose to direct a perfectly placed header high inside Thomas Sorensen's left-hand post from ten yards.
The Arsenal defence still looked rocky when Stoke got the ball into dangerous areas, but the visitors were now in the ascendancy and finished the first half well on top.
Arsenal started the second half with similar dominance and Ramsey could have won a penalty in a tangle with Faye before a shot from Gael Clichy drew a diving stop from Sorensen.
Stoke earned some respite by winning three corners in succession, but it was only temporary as the Gunners upped the tempo again with Emmanuel Eboue's fierce drive forcing another fingertip stop from Sorensen.
The pressure inevitably intensified after Shawcross was sent off and Arsenal made the breakthrough when Pugh handled Bendtner's intended pass and referee Peter Walton pointed to the spot.
Sorensen got a hand to Fabregas' low penalty but couldn't prevent the ball from sneaking inside his left-hand post.
Thomas Vermaelen then prodded a third in the fourth of seven minutes of stoppage time to ensure Stoke were beaten for the first time in 12 games.