The Austrian rider was part of the day's four strong escape group, and with the peloton bearing down on them as they approached the SKODA King of the Mountains climb of Stoke Hill on the outskirts, Brandle attacked to distance his companions.
Shane Archbold and Maarten Wynants valiantly held off the peloton on the fast descent into Exeter to finish second and third, eight seconds down on Brandle, with Sonny Colbrelli leading in what remained of the peloton a further six seconds down.
Omega Pharma Quick-Step's Michal Kwiatkowski came in seventh, safely in the lead pack to retain the Friends Life Yellow Jersey for the second day, with no major changes to the Friends Life General Classification behind him.
The Pole also keeps the Chain Reaction Cycles Points Jersey, with Sky's Ben Swift narrowing the deficit to just three points. Elsewhere Sebastian Lander of BMC Racing retained the YodelDirect Sprints Jersey, while Mark McNally extended his lead in the SKODA King of the Mountains Jersey, picking up points behind the break on both the Mamhead and Haytor climbs.
"We had to chase yesterday, because it is my job I had to go really deep to chase the breakaway back,” said Matthias Brandle speaking afterwards
"Today I got in the breakaway and thought maybe it was possible for a stage win, that's what I tried to do. And finally its happens.
"No one really believed, but then they give us a little bit more and then we chatted some more and now we go full speed ,we started to try and then it was 2'30- 2'40 and it was impossible for them to get us back.
"Finally we really worked well together and it was me who could take the win I had the best legs on the last climb, I tried to push as hard as I could, I managed to break them down and so it was a really nice victory for me but also to win a stage at the Tour of Britain, they are really good guys here and I'm really happy that I could take the win for my team.”
The four rider break of Andreas Stauff (MTN Qhubeka), Shane Archbold (An Post Chain Reaction), Maarten Wynants (Belkin Pro Cycling) and Brandle went within the first few miles of racing from Exmouth, striking out on a venture which would see the latter three never reigned in.
With a maximum lead of just over three minutes, Omega Pharma Quick-Step were content to slowly reel them in, before a large effort by Garmin Sharp brought the lead tumbling down.
On the climb of Stoke Hill it was enough to provoke fireworks from the peloton, with several riders striking out but none being able to bridge the gap to Wynants and Archbold, who continued to chase Brandle all the way to the finish line.
The day's Rouleur Combativity Award was added to the stage victory for Brandle, while IAM Cycling also celebrated further success by moving into the lead of the Friends Life Team Classification, a closely fought affair with the top four teams – IAM, Tinkoff Saxo, Movistar Team and Team Sky – separated by just 30 seconds.
Speaking afterwards, Omega Pharma Quick-Step's Michal Kwiatkowski said;
"We were trying to control that gap to around three minutes, we knew that Brandle had three minutes in the GC so was not a dangerous break away for us. We knew that if someone from another team wants to win the stage they have to take control and chase down the brea away, Garmin did it and I am really thankful to my team mates today they put me out of pressure. Out of the four stages so far this was the first one that I could really relax, it of course was tough, hard with the one kilometre climb and the fast decent into the finish.”
Highlights of Stage Five are on ITV4 at 2000 on Thursday 11 September, with live coverage resuming from 1300 on Friday on ITV4, for Stage Six from Bath to Hemel Hempstead.