An early header from defender Calum Birney would ultimately prove to be the difference as the Sky Blues remain without a point from their first six fixtures.
In a game that had 13 yellow cards, both teams would be reduced to ten men as Mikey Place was first sent off for United, whilst Aaron Rogers also received his marching orders.
However, the Lurgan Blues held on for their first Premiership victory of the season.
"We played 4-4-2 and I just thought we've played 4-3-3 and 3-5-2 and haven't won," he told Glenavon's media channel.
"You have to sometimes look at things, change things up and I thought it worked brilliantly, especially in the first half.
"We created plenty of chances, clear cut ones and we are disappointed we didn't take them.
"I'm glad to get the three points because the boys have worked their socks off.
"It's been a difficult start for them but they've come out today and put in a great performance.
"I thought Jackson Nesbitt was the best player on the pitch today, he led the line, held the ball up, won headers, made life difficult and he deserved a goal."
As the Sky Blues pushed forward for a late equaliser, Hamilton remarked that they shouldn't have been in that position as his side missed chances to put the game to bed.
He added: "We had a lot of quality in the final third in the first-half and sometimes teams with 10 men can make it difficult in the second half and they came into the game more with 10 men and had a bit more fight.
"But, all in all, we had three chances which we should have taken to kill the game off and we should have two or three up, and we wouldn't have been hanging on like we were at the end.
"At 1-0, they can gamble and throw everything forward which they did.
"Thankfully, we stood tall and defended for our lives."