Celtic made three changes to the side that rescued a draw against Aberdeen in the Scottish Cup.
Brown returned from suspension to replace Paul Hartley while defender Lee Naylor had recovered from illness to take over from Darren O'Dea.
Striker Georgios Samaras started for the second time since his loan move from Manchester City in January with Jan Vennegoor of Hesselink dropping to the bench.
United, who play Rangers in the CIS Cup final on Sunday, made six changes to their starting line-up from the side that beat Gretna last weekend.
In came Lee Wilkie, Mark Kerr, Danny Grainger, Craig Conway, Mark De Vries and Michael Kovacevic.
Jan Vennegoor of Hesselink headed over with the goal at his mercy
Sean Dillon, Darren Dods, Willo Flood, Noel Hunt, Christian Kalvenes and Morgaro Gomis dropped out.
Nakamura almost gave Celtic the lead in the third minute, when his left-foot drive from the edge of the box beat Lukasz Zaluska but struck the post.
McDonald also found the wrong side of the post on the half-hour mark after a clever through ball from Brown.
United grew in confidence as the first half progressed and should have opened the scoring 10 minutes before the break.
Conway spurned a great chance for United when he peeled away from Stephen McManus, but headed over Kovacevic's cross from a few yards out.
The home fans grew increasingly anxious after the break as Celtic struggled to breach the United rearguard.
Vennegoor of Hesselink and Barry Robson came on for Samaras and Sno as Celtic searched for a cutting edge.
The Dutchman then headed over from two yards out with the goal at his mercy as United held on to claim a point.
The draw leaves Celtic three points behind their Old Firm rivals having played a game more.
Celtic: Boruc, Hinkel, Caldwell, McManus, Naylor, Nakamura, Scott Brown, Sno (Robson 62), McGeady, McDonald, Samaras (Vennegoor of Hesselink 62). Subs Not Used: Mark Brown, O'Dea, Hartley, Donati, Riordan.
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