The skipper struck a superb free-kick in the second half to extend the Dons' lead at the top of League Two to eight points.
And although Paul Ince's men weren't at their best, it was a deserved victory.
The opening had the feeling of a pre-season friendly as neither team posed a threat in front of goal and the Dons received a boost when the Stags' top goal scorer, Michael Boulding, was taken off after just 15 minutes.
The first chance came to the home side on 20 minutes when Andrews rose highest to meet Dean Lewington's corner and his header was cleared off the line by Gareth Jelleyman.
And minutes later Dons had another headed chance when after a fine move down the left Lloyd Dyer whipped in a tempting ball for Mark Wright, but the winger couldn't keep his effort down.
Things continued at a snail's pace and the Stags could have taken a shock half-time lead when Danny Sleuth had a great chance on 40 minutes, but Willy Gueret did well to beat out his volleyed shot from 15 yards.
Mansfield started the second half brightly and Simon Brown forced a good save from Gueret and had a decent shout for a penalty, but Mathew Hamshaw was shown a yellow card for making too much of Drissa Diallo's sliding tackle.
At the other end Danny Swailes had a decent chance on 56 minutes when he just headed wide from a corner.
Then the deadlock was broken by Andrews on 58 minutes when his superb free-kick from 25 yards could only be pushed on to the crossbar and into the net by Carl Muggleton.
The Dons then tried to finish the game, but to be fair to the Stags they defended well and limited their opportunities.
Lewington had a decent chance after playing a great one-two with Dyer, but he shot straight at Muggleton from 15 yards.
Then on 81 minutes Swailes had a great chance after the ball fell kindly to him in the penalty area, but his volley went straight at Muggleton from ten yards.