A second-half headed goal by Clive Platt proved enough to net maximum spoils and offset the later dismissal of top striker Izale McLeod for a stamping offence.
The result leaves the Pilgrims still struggling towards the wrong end of the table on the back of four losses in the first five outings.
The opening exchanges yielded little to enthuse a sparse crowd. The only moments of enterprise in the first 15 minutes were a long-range off-target drive for MK Dons by Lloyd Dyer and a snapshot by Francis Green for Boston which keeper Adolfo Baines comfortably held.
As the first half progressed the Dons began to mount phases of pressure.
But home centre-back Paul Ellender and Mark Greaves marshalled their backline to good effect.
On 23 minutes another Dons build-up resulted in a 25-yard shooting opportunity for Jon-Paul McGovern, but his effort flew too high.
In reply Boston went close in the 25th minutes when the ball broke to Chris Holland 20 yards out, but his low drive skimmed inches wide.
The Dons returned to the attack in the 38th minute and arguably created their best moment.
Dean Lewington crossed from the left for Aaron Wilbraham to send a far-post header wide of the upright.
And it was aerial strength that brought the visitors a 50th minute lead.
Lewington burst down the left and delivered a pinpoint centre for Platt to head past Andy Marriott from eight yards.
The Dons went close again in the 59th minute when McLeod broke clear. Marriott dashed from goal, but lost out in a challenge with a visiting striker whose low cross shot from an acute angle was headed off the line by Tim Ryan.
Boston tried to find a response and threw on Bob Davidson and David Farrell in a bid to trigger more attacking life.
However, long-range shots from Dany N'Guessan and Green flew off target.
The visitors' mission was made harder in the 78th minute when star striker McLeod was sent off for a needless stamp on Ellender, after the home defender had won possession in a challenge close to the halfway line.
As stoppage time kicked in Boston almost drew level when a raking cross by Ryan found substitute Davidson at the far post, but his header flashed inches off target.