After Garry O'Connor had given Hibs a sixth-minute lead, Craig Beattie leveled for the Hoops who had been hoping to open an eight-point lead at the top of the Premier League standings.
But Sproule, an Irishman in his first season in the top flight of Scottish soccer, restored Hibernian's lead in the 79th minute and Brown added a third in the 81st.
The surprising loss at home means that Martin O'Neill's team are still five points ahead of Rangers. But the 'Gers can cut that to two by winning at Aberdeen today.
Hibs' victory means that Tony Mowbray's players cemented their position in third place and stayed on course for a spot in next season's UEFA Cup.
Bayern Munich romped to a 4-0 win against FC Kaiserslautern to seal a record 18th Bundesliga title.
Dutch forward Roy Makaay recorded a hat trick for Bayern as Schalke was eliminated from the title race with a 3-3 draw against Bayer Leverkusen. The second-placed team fell 11 points behind Bayern with three rounds to play.
"This is my fifth title and one of the best -- I hope we can make it a double with the German Cup," said French defender Bixente Lizarazu.
The Bayern players, after waiting to see if Schalke scored a late goal, then ran onto Kaiserslautern's pitch with giant Bavarian mugs and doused each other in beer.
Bayern coasted to its sixth straight win after Germany midfielder Michael Ballack netted a low shot off Makaay's 19th-minute backheel inside the post.
Makaay added goals in the 35th, 48th and 68th minutes for Bayern, which won its 19th German title.
The Bavarians won in 1932, before the Bundesliga was formed for the 1963-1964 season.
"It's a real relief, a real joy to finally win a title," said Bayern's rookie coach, Felix Magath.
Schalke appeared set to extend the race another week when it took a 3-1 lead against Leverkusen on two free-kick goals by Lincoln and a 41st-minute score by Danish striker Ebbe Sand.
ButSchalke self-destructed. Leverkusen's Dimitar Berbatov got one back in the 56th minute with a deflected shot and Andrei Voronin's chip over the 'keeper eight minutes later leveled the match.
Defender Jean-Christophe Devaux scored with a stunning late free kick as Strasbourg beat Caen 2-1 to win the French League Cup.
With 11 minutes remaining, Mickael Pagis tapped the ball to Devaux and he thumped a ferocious shot into the roof of the net after Caen had come back from a goal down.
The win secured Strasbourg a place in next season's UEFA Cup and gave the Alsace club its second League Cup title in eight years.
"I told my players to give their maximum and I have to say thanks to the fans for all the help you gave us," Strasbourg coach Jacky Dugueperoux said.
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