Antony Kay gave MK Dons the lead after the break when he headed Robert Hall's corner but Clucas restored parity directly from a curling set-piece.
In a first half of few chances, Hull came closest when Mohamed Diame headed Isaac Hayden's cross just wide.
Diame tried his luck again with a neat turn and shot in the box but he fired straight at Dons keeper David Martin.
The result means Hull move above Brighton into third place in the Championship, but have recorded just one win in their last seven matches in all competitions.
Steve Bruce's side could have leapfrogged Middlesbrough and moved into the top two with a win by virtue of goal difference.
MK Dons, who have never won against Hull, remain in 21st place and a point above the relegation zone.
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Hull City manager Steve Bruce:
"We're frustrated but we didn't play anywhere near well enough in the first half. We've played better in the second half.
"First half we didn't move the ball quick enough and gave the ball away in bad areas.
"At the end of the day I pick the team but I scratch my head and ask why we've played like that in the first half. We've got to take away the nerves and a little bit of edginess which may be creeping in."
MK Dons manager Karl Robinson:
"I thought it was a handball that led to it [Sam Clucas' goal]. They are a team, the officials, and referees get slated up and down the country. As a group of four they should be judged and he wasn't assisted right today and that was disappointing.
"I thought there were two completely different halves. I thought the first half we dominated and moved the ball unbelievably well.
"For a team where we are to come to the KC Stadium and perform the way we did was excellent. Second half, playing one of the best teams in the league, we knew how hard it was always going to be. I thought my players' application was sensational."

In a report going to board members next week, finance director Nick Kenton said the forecast gives "significant cause for concern".
However, he said there was time to breakeven by the end of financial year.
Raigmore Hospital in Inverness accounts for £10.5m of the potential projected overspend.
Mr Kenton said "significant effort" was needed to achieve "financial break even" and avoid the potential £15.6m overspend by the end of March next year.
Waiting list initiatives, nursing reviews and the use of medical locums have been identified as causes behind the overspend at Raigmore, the largest hospital in the Highlands.
Board members are due to discuss the matter on Tuesday.
In a statement, the health board said: "The £15.6m overspend is a potential projected figure based on the first three months of the financial year and while the board appreciates that it will take a significant effort to achieve financial breakeven, NHS Highland remains confident that there is sufficient time remaining in the financial year to allow the breakeven target to be met."
At the end of the last financial year in April the health board had to ask the Scottish government for a £2m loan to balance its books.
Sam Clucas' second-half free-kick gave promotion-chasing Hull a point as they drew with lowly MK Dons.
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NHS Highland has forecast a potential £15.6m overspend based on the first three months of the financial year, but said it expects to break even.