The team of Philip Hindes, Jason Kenny and Callum Skinner clinched the medal with a time of 42.44 seconds - a new Olympic record - ahead of world champions New Zealand who finished in 42.54 seconds. France took the bronze against Australia with a time of 43.143.
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The night started well for the Brits who qualified in 42.562 seconds - half a second quicker than even they had hoped to, and a tenth of a second above the second-placed Kiwis.
"All of it was a surprise today, genuinely. We surpassed ourselves. Then I thought we could run away with it, but New Zealand gave us a run," Kenny said.
"We went into the finals with nothing to lose. We left it on the track, and unbelievably it was enough to win the gold. We can't win the bloody worlds to save our lives, but we win the Olympics every time."
It beat the 42.600 Britain set when winning gold in the 2012 London games, though was later bested by New Zealand in the first round, finishing in 42.535 seconds.
And it was just one of many successes for Great Britain in their first night on the track.

Britain's Laura Trott (R) and Britain's Katie Archibald celebrate after breaking a world record during the women's Team Pursuit qualifying track cycling event at the Velodrome during the Rio 2016 Olympic Games in Rio de Janeiro on August 11, 2016.

Image credit: AFP

The women's pursuit team went through the first round of the team pursuit qualifiers in style, setting a new world record as they did so.
Finishing in 4:13.260, Laura Trott, Katie Archibald, Elinor Barker and Joanna Roswell-Shand set themselves up as strong contenders in the competition.
In Sir Bradley Wiggins return to the track in the men's team pursuit qualifying stage, finished just outside world record-breaking time in 3:51.943 to top the leader board by over three-and-a-half seconds.
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