Emersonn's early header was cancelled out by a stunning Nilson Angulo free-kick before Clarke settled the contest at Portman Road, condemning Régis Le Bris' side to defeat in Gary O'Neil's first competitive match in charge of Ipswich.
Le Bris, speaking to BBC Match of the Day, felt Sunderland had struggled to break down a well-organised home side.
"We had the possession but we had to find solutions to break their block. We tried, we created a few chances but we were not clinical enough."
Asked whether the display reflected early-season rustiness, the Frenchman pointed to the cost of individual mistakes against sharp opposition.
"It is often the case. It is not unusual. Today it was massive because of the consequence but this is the Premier League, it is ruthless. We have to lift our level when we are in this situation. Winning is important but it is also about the style of play. Our regret is more about us because we made those mistakes. It is a process. We will learn from this experience."
Ipswich Town manager Gary O'Neil, speaking to BBC Match of the Day, said his side had refused to settle for a point even when the game was level.
"We were never going to settle for 1-1, even if 1-1 would have been a good result for us against a good Sunderland side. For our goal to come from a pressure phase that late in the game shows the togetherness, fitness and work-rate of the players."
He credited his substitutes, including matchwinner Clarke, for maintaining the intensity of the press.
"The subs really helped, fresh energy, three of them, maybe four of them, involved in the pressing phase at the end. We wouldn't have been able to do that if we only had our starting XI. It's going to take everyone at this football club pushing together to get us results like today."
O'Neil felt his side had deserved the win on balance.
"I'm pleased, I thought we deserved to win. On the balance I know Sunderland had a lot of the ball. They scored a world class goal to get back in it. But I'm really pleased with our players, they were excellent to a man."
On the pressing plan that set up the win, he explained: "We tried to get the ball to that side of the pitch, all afternoon. If you watch all of our pressing phases we try to get the ball to their left, we try to be aggressive. I thought the second goal showed good team understanding and the first one was unbelievable quality from Julio Enciso."
Man of the match Enciso, on loan at Ipswich last season before his permanent move, drew particular praise. "We worked our socks off to sign him, not only does he bring those moments of magic, his work ethic and ability to defend, to stop Xhaka finding his rhythm, there's not that many number 10s that have his quality and can do that side of it. He's special in that way."
O'Neil admitted Angulo's leveller had brought back painful memories of his own top-flight playing days.
"It felt like a welcome back to the Premier League. You're 1-0 up, looking comfortable and someone smashes a free-kick in from 25 yards and I was like 'I remember what this is like'. It's tough. To just win one Premier League game is tough."