On-loan Sunderland striker Graham stabbed home a spilled shot from close range midway through the first half - Boro's first goal in eight games - then headed a second just before the break.
And after the opener the £5m striker buzzed about and created all kinds of problems for the Town defence as Boro played with the shackles off.
"I was happy for Danny," said Karanka. "After the goal he demonstrated he is a very good Premier League player.
"He showed exactly the kind of player he is with typical striker's goals from close range. I'm happy for him because he deserves to score.
"He came here to help us and I know he had a long time without a goal. It's good for him to score because strikers thrive on confidence and that will do him a power of good.
"He could be forgiven for thinking he's more important than the other players here because he's come from the Premier League, but he's a very humble hard-working player who deserves his rewards."
And the Boro boss admitted he was relieved to end a barren spell - but insisted he was never worried.
"Finally, the goals arrived and I'm very happy. Firstly, our supporters deserved to see us scoring goals and winning and secondly it's great for my team to reward their hard work," he said.
"But I was never worried. I always believed 100 per cent in myself and in the team and I know that when we work hard and play like that we can beat anybody."
Scathing Ipswich boss Mick McCarthy admitted his team got what they deserved.
"We were second best, we got nothing and deserved nothing," he said.
"We didn't compete and that wasn't like us. If I knew why I'd put it immediately right. We've had a bit of a broken week with internationals, I could give you a whole host of reasons.
"I actually think Middlesbrough played well and when they got the goal they got on top and didn't let us play.
"They've got a fair few quid in that team with the likes of Graham, Tomlin and Leadbitter who we couldn't afford to keep. They've got a good side and we've got to play well to stop them, but we didn't play.
"The second goal was awful marking on our part. It was a bad day at the office. You can ask me to put meat on the bones of that, but I think bad day at the office sums it up.
"We've not performed so I can't take any silver lining from other results. To be in with any chance of getting into the play-offs, we need to be much better than that."