Beckett was Gainsborough's top scorer this season with 17 goals
Gainsborough Trinity beat Harrogate Town 3-2 in their final game of the season in Blue Square North on Saturday to end a run of 11 games without a win.
Luke Beckett set up Ryan Mallon for Trinity's opener before Jamie Smith equalised against his former club.
Chris Hall restored the lead after 52 minutes but Nicky Gray pulled Harrogate level again in the 68th minute.
But Beckett had the final word four minutes later, scoring the winner from the penalty spot.
Gainsborough manager Steve Charles told BBC Radio Lincolnshire: "Again we've given a couple of bad goals away, but Harrogate are a decent side so it's nice to have done the double over them."
Having been within touching distance of the play-off places in February, Trinity ended the season in 13th place in Charles' first full season in charge at the Northolme.
He admitted: "I've enjoyed it, though it's been hard work at times. I'm disappointed with where we've finished but it's a learning curve.
"We've stumbled at times, at home, but we will get stronger and hopefully we'll keep our good away record and put the home record right next season."
In the Unibond Premier Division Jon Froggatt's sixth-minute penalty was enough to give Boston United a 1-0 win over Cammell Laird and guarantee the Pilgrims' safety.
Danny Brooks scored from inside his own half as Grantham Town beat Gresley Rovers 2-0 in the Unibond First Division South, with Lee Beeson also on target.
Sean Cann's 21st league goal of the season was little more than a consolation for Lincoln United in their 4-1 defeat by Kidsgrove Athletic, Spalding United went down 2-0 at Carlton Town and Stamford beat Glapwell 3-1 with goals from Dan Cotton, Ben Easson and Nick Kirk.
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