Yeovil boss Gary Johnson hailed a "hugely significant win" after a dramatic 90th-minute own-goal by substitute David Hunt gave his men a 1-0 victory at high-flying Crawley.
The Glovers were forced to ride their luck at the Broadfield Stadium with Crawley twice being denied by the woodwork, while they had two efforts cleared off the line in the second half.
Yeovil faced Crawley off the back of a 4-1 defeat at Swindon and Johnson said: "You can see why Crawley are where they are in the table.
"They are a decent team and of course they created chances but we were brave throughout.
"It is a hugely significant win for us as before tonight we hadn't beaten a side in the top six."
Johnson felt opposite number Richie Barker could have been more gracious in defeat and admitted: "Their manager told me how lucky we were at the end.
"Last Saturday I had Paolo Di Canio (Swindon manager) saying that they should have scored eight and now he (Barker) said we were really lucky.
"It would have been nice to have had a pat on the back and been told well done."
Crawley have now not won in five games but Barker was satisfied with his side's performance following last Saturday's 2-2 draw at home to Walsall.
He said: "There are 20 games to go and you get highs and lows like this all season. The important thing is how you react to them."