The 31-year-old Scotland international, who has been promoted four times in his career, agreed a two-year contract with the Clarets last month.
He scored his first goal for the club in Tuesday's 5-0 win over Gombak United in Singapore, heading home a pinpoint cross from winger Chris Eagles.
"I'm delighted to be off the mark and hopefully it will be the first of many," said Iwelumo.
"It was a fantastic cross and if that's the service I'm going to get then hopefully there will be lots of goals.
"I'm buzzing and it was a really good decision to come here. They are a great bunch of lads and although there's a lot of hard work to do I feel we are nearly there."