The win for Town ensured they held on to the final automatic spot in League Two.
Scott Neilson was the hero of the hour, netting the only goal in the 67th minute to send Crawley up with champions Swindon and Shrewsbury.
At the other end of the table there was heartbreak for Hereford, who beat promotion contenders Torquay 3-2 but saw their six-year stay in the Football League come to an end.
Had Crawley slipped up, Torquay were one of the teams in a position to take advantage but they were three down inside 40 minutes through goals from Delroy Facey, a Harry Pell penalty and Robert Purdie.
Ryan Jarvis and Taiwo Atieno pulled goals back for Torquay in the second half but, although Hereford held on, it was not enough as Barnet beat Burton 2-1 at the Pirelli Stadium.
The visitors made the perfect start with Mark Byrne's sixth-minute goal but their Football League status was very much in doubt when Jacques Maghoma equalised and then Calvin Zola drilled a penalty over the bar.
The all important second goal came from captain Mark Hughes, who restored Barnet's lead on the hour mark and ensured they finished the season two points clear of the relegation zone.
Like Torquay, Southend also had to settle for a place in the play-offs, although they did leapfrog the Gulls into third place with a 2-0 victory over bottom side Macclesfield, Peter Gilbert and Neil Harris scoring the goals.
Crewe made certain of taking the final play-off place with a 2-2 draw against Aldershot, who had responded to an early goal from Ajay Leitch-Smith by taking the lead through Harry Davis and Mark Molesley before Luke Murphy levelled matters again 14 minutes from time.
Oxford were the only team who could have overtaken Crewe but they were thumped 3-0 by Port Vale, for whom Marc Richards, Sean Rigg and Ben Williamson netted.
Swindon ended a brilliant season in forgettable fashion with a 0-0 draw at Bradford, while Shrewsbury headed for League One with a 3-1 defeat by AFC Wimbledon, where all the goals came in 14 minutes at the start of the second half.
Byron Harrison and Luke Moore put the hosts two up and, although Shane Cansdell-Sherriff pulled one back, Moore restored the advantage with his second.
Gillingham hit the 70-point mark, two short of the play-offs, courtesy of a 2-0 victory over Morecambe, while the biggest winners of the final day were Dagenham & Redbridge, who thumped Bristol Rovers 4-0.
Plymouth finished a difficult season with a 2-1 defeat against Cheltenham, although safety was always their objective, while Rotherham and Northampton drew 1-1.