Clarets boss Howe, who has lost just one of his six games in charge, sent on Thompson in the 74th minute after seeing his in-form side create and miss numerous chances as they trailed to Michael Chopra's opener for Cardiff in first-half stoppage time.
And just as it looked as though Cardiff were going to hold on and climb to within three points of Championship leaders QPR, Thompson glanced home Ross Wallace's corner to finally haul the visitors level in the 83rd minute.
Cardiff extended their unbeaten league run to seven games since back-to-back defeats at the turn of the year, but played second fiddle for long periods to Burnley, who have climbed to within five points of the play-offs.
Cardiff could have been two goals ahead inside 13 minutes, but were denied first by the woodwork and then Burnley goalkeeper Lee Grant.
Chopra's seventh-minute shot from a central position on the edge of the penalty area hit the crossbar and Grant pulled off a fine save at full stretch to keep out Peter Whittingham's left-footed curler soon after.
Burnley responded with their first shot on target through Chris Eagles, but his 20-yard effort was comfortably held by Cardiff goalkeeper Tom Heaton.
Clarets midfielder Jack Cork and Eagles again were both off target with long-range shots as Burnley wrestled back an equal share of possession.
Eagles was relishing his role in the visitors' midfield and forced Heaton into two more saves in quick succession with a 30-yard thunderbolt and then an angled drive from inside the area as Burnley dominated proceedings.
Another shot from Eagles was blocked by Cardiff defender Mark Hudson, but after spending long periods on the back foot, Cardiff snatched the lead just before the break.
Jay Bothroyd raced clear down the right and his excellent ball across the six-yard area was slammed home into the top corner by Chopra for his ninth goal of the season.
Burnley started the second half positively. Eagles had one effort blocked by Bothroyd and another held by Heaton, while Wallace flashed a 25-yard drive wide as the visitors chased an equaliser.
Charlie Austin stepped off the bench to make his third appearance for Burnley following his recent move from Swindon in place of Chris Iwelumo, while Chopra made way for Cardiff talisman Craig Bellamy.
Burnley boss Howe then sent on Thompson for Jay Rodriguez in the 74th minute in a bid to force an elusive equaliser.
Cardiff soaked up the pressure and broke out to create another golden chance, Bothroyd pouncing in the area to force Grant into a fine save from close range.
But the Clarets were not to be denied and finally got back on level terms in the 83rd minute when Thompson reacted quickest to Wallace's near-post corner to send a glancing header beyond Heaton into the bottom corner.
Eagles lashed a 30-yard shot over the crossbar soon after the restart but both sides settled for a point.