Having been torn apart on their way to a 4-0 defeat at Newport County last weekend, Town manager Simon Weaver and his assistant Thirlwell opted to try out a 3-4-3 system that saw them line up with three central defenders and George Thomson and Lewis Page operating as wing-backs.
And Harrogate's number two, who took charge of proceedings due to Weaver's Covid-enforced absence from the EnviroVent Stadium, was thrilled with what he saw.
"When you lose a game in the manner which we did last week, the gaffer and I were talking straight away about what we could do moving forwards," Thirlwell said.
"We both thought that this [formation] was something that could work for us for this particular game and we worked on it all week and really got after the lads in terms of what we were looking for.
"We looked at the squad and, the way we played today, we do have good options to play this system. You have to be adaptable and you can't get stuck in the mindset of playing the same way all of the time.
"So this is the way we went today and it has worked for us. But, all the credit goes to the players because they are the ones who had to go over the white line and perform the way that they did after a performance that wasn't good enough last week.
"The lads were magnificent today. There's always moments where you can do better in games, but generally I thought it was a great performance."
Muldoon broke the deadlock after 17 minutes of Saturday's contest when he demonstrated his predatory instincts inside the Oldham box to convert Page's inviting cross from the left.
Town's versatile forward doubled their advantage in the 73rd minute, running through on goal and finishing confidently beyond Jayson Leutwiler having been set up by Brahima Diarra.
The 32-year-old then completed his treble, taking his tally to the season to 10 in the process with a classy curling finish into the top corner.
And although Thirlwell said that nobody in the Harrogate camp will be getting too carried away off the back of what is a long-overdue success, he insisted that his players deserve credit for the quality of the football they served up.
"The result is the be-all and end-all, that's football," he added.
"But, to marry it up with a really good performance, that's what everybody wants. You want to win, but you want to win playing well.
"Oldham have had two really good away points at Barrow and Hartlepool and been really tough to break down. They scored five against [top-of-the-table] Forest Green not long ago, so they are no mugs even though they are in a difficult position at the moment.
"I'm sure they will start winning games, but it was all about us today and what we did and I think the lads did ever so well."
Victory sees Town climb three places in the League Two standings and up to 11th position.