Rovers started the day three points above the bottom two but their defeat, combined with victories for both Wycombe and Northampton, saw the Pirates' 94-year stay in the Football League brought to an end.
Colin Daniel's first-half volley proved enough for Mansfield as Rovers hit the crossbar three times but were denied the equaliser they so desperately needed.
The final whistle was greeted with a chorus of boos and a number of home fans entered the pitch to express their anger.
It was only a difference of three goals that saved Wycombe, who won 3-0 against already-relegated Torquay.
Sam Wood opened the scoring for Wanderers in the sixth minute before Steven Craig doubled the advantage from the penalty spot shortly before the interval.
Torquay had Anthony O'Connor sent off and Matt McClure wrapped up the win with a third as the visiting fans then had to hope Mansfield held on.
Northampton finished with a worse goal difference than Rovers but survived three points clear after a 3-1 victory at home to Oxford.
Oxford set the Northampton nerves jangling when Ryan Williams put the visitors ahead early on but Williams turned from hero to villain when he was sent off soon after.
The Cobblers took full advantage of the extra man as John Marquis, Ivan Toney and Mathias Doumbe scored to ensure a vital win.
At the other end of the table, Chesterfield capped off their promotion season by being crowned champions after a 2-1 win at home to Fleetwood, who finish fourth.
The league winners had to come from behind as Sam Hird and Gary Roberts overturned Matty Blair's first-half opener.
Chesterfield beat second-placed Scunthorpe to top spot after the Iron were held to a 2-2 draw at home to York.
The hosts surrendered a two-goal lead as Paddy Madden and Terry Hawkridge's efforts were cancelled out by York's Ryan Brobbel and Will Hayhurst.
The draw means York finish seventh and will now meet Fleetwood in the play-off semi-finals.
Third-placed Rochdale will be joining Chesterfield and Scunthorpe in League One next season despite a 2-1 defeat at Newport.
Rochdale, who had already sealed automatic promotion before kick-off, could have taken all three points and second place as Matthew Lund missed an 83rd-minute penalty with the score 1-1.
George Donnelly had earlier put the visitors in front before Aaron O'Connor drew Newport level.
The hosts were reduced to 10 men after Ryan Jackson brought down Ian Henderson in the area but Lund was unable to capitalise from the spot.
Kevin Feely then made Lund and Rochdale pay the price as he headed in an 88th-minute winner.
In a dress-rehearsal for the play-off semi-finals, Southend beat Burton 1-0 to climb above their promotion rivals into fifth on goal difference.
Barry Corr's first-half winner means the two teams both finish on 72 points and will meet again for the first leg of the knock-outs next Sunday.
Wimbledon dropped to 20th in the table after a 3-2 defeat at Accrington.
The hosts were three up early in the second half thanks to Kayode Odejayi's opener and James Gray's double.
Wimbledon staged a comeback as Jack Midson scored a penalty and Kwesi Appiah added a second late on but it was not enough to avoid defeat.
Portsmouth and Plymouth were forced to share the spoils after a thrilling 3-3 draw.
The two sides shared four goals in nine minutes before half-time as Pompey twice led through Danny Hollands but were pegged back by Reuben Reid and Conor Hourihane.
Portsmouth restored their lead when Hollands completed his hat-trick early in the second half but there was a late twist as Hourihane made it 3-3 with one minute to play.
Cheltenham ended the season with a fourth defeat in a row as they lost 3-2 at home to Dagenham & Redbridge.
Steve Elliot and Matt Richards put Cheltenham ahead twice in the first half but Sido Jombati's own goal and Scott Doe levelled the score before Adebayo Azeez found the net for the visitors in the second period.
Jimmy Keohane and David Wheeler steered Exeter to a 2-0 victory over Hartlepool, for whom Jack Compton missed a penalty, while Morecambe and Bury played out a goalless draw.