Blackburn's victory handed Chelsea, who secured their second successive Premier League title on Saturday, their fourth league defeat of the season and sparked huge celebrations at a packed Ewood Park.
Reid's 43rd minute effort moved sixth-placed Blackburn to 60 points and ensured their nearest rivals Newcastle United, who are on 55, cannot overtake them with only one game remaining.
"We're delighted and it's been a huge effort and sometimes you don't get what you deserve but tonight we got what we deserved," Blackburn coach Mark Hughes told Sky Sports.
"This season we've built on the qualities we showed last season and we're in Europe now and we'll see how far we can progress next season."
Jose Mourinho made eight changes to the side that clinched the title three days ago and it showed early on as they struggled to make an impact in the first half.
David Bentley missed a great chance to put Blackburn ahead in the 28th minute when his deflected header shot past an open goal.
At the other end, a left-footed effort from a sliding Eidur Gudjohnsen hit the post seven minutes later after Geremi put in a great pass in front of the Icelandic striker.
But Reid was quick to point out that he was the last man to have had any contact with the ball, jumping up from the crowded area in the box to nod in the header.
Unaware Reid had got the final touch, Savage rushed to rejoice with the fans and was shown a yellow card for his over-zealous celebrations.
Reid limped off in the 70th minute and had to be substituted when he pulled up clutching his back after turning awkwardly on his ankle.
Chelsea enjoyed most of the possession following the interval but keeper Brad Friedel preserved Rovers' lead with his athletic saves.
The London club were denied a penalty after Blackburn substitute Aaron Mokoena tugged Hernan Crespo to the ground in the box but the incident went unpunished.
"Blackburn deserve to be in UEFA Cup but they didn't deserve to win like this," said a disgruntled Mourinho.
"We deserved two, maybe even three penalties but (not being given) the Crespo penalty was ridiculous as the lineman was in front."