The six-man British crew, steered by Ben Ainslie, won by 30 seconds to end a run of four straight defeats.
Ainslie’s Land Rover BAR team now have two wins from their six races – both against Sweden.
The result means Britain stay in third place on four points, two clear of Sweden, France and Japan.
New Zealand are in second, while the United States top the standings.
“We made some big changes to the boat and we had a great race,” said Ainslie, whose crew take on New Zealand and France on Wednesday.
It’s a big win for us but we need to keep looking forward.
Standings and how it works
|America’s Cup Qualifiers|
- *Land Rover BAR started the round-robin qualifiers with two points and Oracle Team USA with one point after finishing first and second respectively in the 2015-16 World Series
- Each team races the other teams twice in this stage, gaining one point per victory, with the top four progressing
- Defending champions USA skip the next stage and advance automatically to the America’s Cup matches
What about the rest of the field?
Sweden led for the majority of their race against New Zealand but the Kiwis took advantage of a late slip-up for victory.
In Tuesday’s other race on the Great Sound, the United States comfortably beat France, who were almost two minutes adrift.
Wednesday, 31 May
Race 4 – Japan v France, Race 5 – Great Britain v New Zealand, Race 6 – United States v Japan, Race 7 – France v Great Britain
What happens next?
The top four qualifiers are split into two best-of-five semi-finals from 4 June, with the winners competing in the final for the right to take on holders Oracle Team USA, who advance automatically to the actual America’s Cup matches.
The first to seven points wins the America’s Cup, or the Auld Mug as the trophy is known, with a possible 13 races to be sailed on 17-18 and 24-27 June.
The America’s Cup, the oldest competition in international sport, was first raced in 1851 around the Isle of Wight and has only been won by four nations.