Achara scored 13 points for GB, along with Nate Reinking
Great Britain registered their first win of the summer when they outlasted Slovenia 63-56 in their final game of the Seville tournament.
Kieron Achara and Nate Reinking had 13 points each for GB and Andrew Betts added 12 points and six rebounds.
In a defensive contest that was always close and occasionally dour, GB took the lead for the last time on a basket from Achara with 4:20 remaining.
Reinking then added a three-pointer in the last two minutes.
GB's win was an unlikely one in view of the previous night's comprehensive defeat by Lithuania.
In addition, Joel Freeland, the team's best player so far this summer, missed the game to rest a shoulder injury and Robert Archibald also sat out the action.
It's a combination of joy and relief, we just wanted to get a win,
Point guard Flinder Boyd decided to take a chance on his injured ankle and played a part in keeping GB close in the first half, when Slovenia took a 20-11 lead.
Reinking's three-pointer in the third quarter levelled the scores at 27-27 and another at the end of the quarter gave GB a 44-43 lead.
He then tied up the game again with a pair of free throws with 4:45 remaining before Achara hit four points in a row to give GB a four-point cushion.
Reinking's three with 1:54 left on the clock and pair of Mike Lenzly free throws then ensured Chris Finch's team got the win they desperately needed after five straight defeats.
"It's a combination of joy and relief, we just wanted to get a win," said Betts after the game.
"I was only sure we'd got it right at the end - I wasn't comfortable until we had a five or six-point lead."
Finch, who admitted he had thought of holding Betts out of the game, added: "Andy was huge - he gave us composure down the stretch."
The coach also praised Scottish forward Achara, one of the team's most improved players, who registered his highest international score for his country.
"He works really hard and he's got a feel now for how to play the European game," said Finch.
The team had further reason to celebrate with the news that forward Pops Mensah-Bonsu is also likely to return to the team in time for Wednesday's trip to Turkey after resolving his NBA contractual status, agreeing to join the Houston Rockets.
"Pops is going to be a big addition - he gives us a ton of energy," added Finch.