Steve Clarke felt his Scotland side ended their long wait for a win with arguably their poorest performance of the UEFA Nations League campaign – but were due the break they received from Croatia’s disputed red card.
Croatia looked the more dangerous side until Petar Sucic received a second yellow card in the 44th minute for a lazy studs-up challenge on John Souttar, having earlier been booked for an innocuous foul on Billy Gilmour.
Scotland's final ball let them down as they tried to force home the numerical advantage and Croatia even had the best second-half chance before substitute John McGinn knocked home the only goal in the 86th minute.
Scotland remain bottom of section A1 but will avoid automatic relegation if they win in Warsaw on Monday against a Poland side fresh from a 5-1 defeat against group winners Portugal.
Clarke, whose side went 10 competitive matches without victory, said: "It's nice to have a win on the board in a competitive match.
"Really pleased with the players, the effort they've put in up until now. They deserve more points and it's nice to get that win.
"I think we can be better with the ball, I think we can be more clinical when we get to the final third. Obviously the sending-off changes the direction of the game. But we were due a little break.
"We've been building performances. If I'm being honest, I think tonight was probably one of our poorest performances out of the five games we've played so far. But we got the little breaks that fell in our favour and we managed to turn that into a win."
Clarke's side have even given themselves an outside chance of finishing second, which would send them into the quarter-finals and pot one of next month's World Cup qualifying draw, as well as ensuring they stay in the elite level of the Nations League.
As well as beating Poland, Scotland would need Portugal to win in Croatia with at least one of the victories by a margin of two goals or more.
Clarke is not thinking of goal difference.
"We have to win," he said. "First job is to go there and win. If we do that then we'll count up the goals and whatever afterwards.
"But let's take it a step at a time. It's been a hell of a long time since we've got a win. Now we've got to get another one on Monday night."
Clarke revealed he started McGinn on the bench because of how Ben Doak and Ryan Christie played last month when the Aston Villa midfielder was injured.
"But I also knew that I was strengthening the bench a little bit," he added. "You've got John to come in, and he does what he does. He comes off the bench and scores the winner."
McGinn's chance came from a saved shot from Doak, whose direct running was Scotland's most potent threat.
"He was good but I thought he might be," Clarke said. "He's come into the team, he's shown a really positive attitude.
"He brings us something a little bit different to what we've had before. So really pleased with Ben. He gets the assist for the goal, could maybe have a couple more, could maybe have scored one himself.
"That's a contribution from a young player that we need to protect and look after. We realise that he's good for now and hopefully for a long time in the future."
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