The Tannadice centre-back produced a largely solid showing in the Tangerines’ Premiership opener against the Dee, aside from the moment he was spun by Simon Murray before conceding a penalty kick in his desperation to make amends.
Luke McCowan made no mistake from 12 yards to rescue 2-2 draw for the Dark Blues.
Having been left out against Ross County in the Terrors’ next league game, Sunday’s showdown with St Mirren marked his first opportunity to put that set-back behind him – and Graham obliged by heading home the only goal of the game.
And defensively, he barely put a foot wrong as United kept their second clean sheet of the season.
“Football is always going to have ups and downs,” said Graham, reflecting on derby day.
“You’re going to make mistakes and, unfortunately, that mistake got punished.
“That’s how it’s going to be at this level. Every mistake you make is more than likely to get punished. I’ll learn from that.
“The manager took me out last week and he explained the reasons to me. He wanted me to show a reaction (against St Mirren) and I felt like I did.”
United’s answer to Rory Delap?
Reflecting on his fourth senior goal for his boyhood heroes, Graham added: “We work on our set-plays and looked for weaknesses in their defence. It was all about the delivery into the box.
“It was a good ball by Will (Ferry). Thankfully, I got myself on the end of it.”
While providing a goal threat at one end of the pitch and a roadblock at the other, Graham also served as an unlikely supply line courtesy of his booming long throws.
Several missiles into the box caused havoc and one, bizarrely, struck the bar after evading everyone.
“Nobody touched it, so somebody asked the ref what would happen – but he said it would have been no goal,” continued Graham. “I was hoping someone would get on the end of it but unfortunately not.
“If you get the ball in the box, it can cause problems for the other team’s defence, so I try to help out in as many ways as possible. If you have a long throw you need to use it to your advantage.
“We practice set-plays and I chuck a couple in through the week.”
Graham: New look United need to stick together
The Terrors have been paired with Motherwell in the quarter-finals of the Premier Sports Cup but that encounter will be immediately put on the back-burner given the importance of Saturday’s visit of St Johnstone.
And Graham reckons United’s start to the season provides plenty of cause for optimism.
“We more than matched Dundee – a top-six side – in the first league game,” added Graham. “County are a good, steady side and physical. We more than matched them as well.
“On Sunday against St Mirren, who have been top six for the last two seasons, we competed and got the win.
“We’re a fairly new side with a lot of new faces in the building. We need to stick together, and we’ve done that.”