The Ivory Coast midfielder settled the match in the 64th minute, heading home from close range after Costinha directed a ball back across goal.
Getafe had threatened earlier, with Jaouen Hadjam hitting the woodwork twice, but Brighton held firm to claim their third consecutive clean sheet in the competition.
The result was particularly welcome for Hürzeler, whose side had found it difficult to break down José Bordalás's organised defence.
"These games in the Conference League are different. You have to beat a low block. You have to understand what the opponents are looking for in the game," the Brighton manager told TNT Sports.
"Therefore, you have to always be patient in these games and I think we did it today.
"We didn't play our best game, to be fair. We had a few moments where we were quite lazy with the easy things. We didn't do the simple things on the highest level but in the end we kept a clean sheet, third clean sheet in a row in this tournament and we scored a goal and I think we deserved to win this game."
Bordalás felt Getafe had performed well for long periods but admitted his players had struggled physically as the match progressed.
"We're not happy. The team had a great first half and stayed in the game," he said.
"They had more freshness. We paid for the effort we've been making from the beginning, with players who were already struggling, and that goal hurt us a lot.
"We were facing a great team, we knew it would be difficult. We know it's difficult to qualify for the next round, there are three games left and not everything is decided yet."
The Getafe manager was particularly frustrated by another defensive lapse, having seen his team concede in most of their European matches.
"I'm partly happy, but not completely because we haven't won and, above all, because we've conceded again," he said.
"We have to correct that aspect. We've only managed two clean sheets. The rest of the Conference League matches and the qualifying round, we've conceded. It's very difficult like that; you're not always going to score goals.
"It was a very serious mistake that we had been warning about and it cost us the defeat."
Bordalás also highlighted the difference in resources between the clubs, claiming Getafe were operating with a much smaller squad than their Premier League opponents.
"We're going to try to recover the players. We felt it in the final stages, from around the 70th minute, when they were running out of energy," he added.
Hürzeler, meanwhile, was pleased with the contribution of Pascal Groß, who was substituted after another demanding appearance.
"At one point we need to manage him as well, but at the moment he just keeps running. He seems to be in a good shape. Today he didn't play the full 90 minutes, also manage the energy from the players like this."
Brighton remain in a strong position in the league phase, and Hürzeler encouraged supporters to keep dreaming about a possible European triumph.
"They should dream, that's what I always say. We focus on work. We focus on the things we can control. They should dream and hopefully at one point we can fulfil their dream."