A cagey opening 15 minutes saw both sides playing good football, but unable to create any clear-cut chances.
Luton had a great opportunity to break the deadlock moments later, skipper Zara Carroll’s effort from distance parried into the path of Amy Summerfield, who hooked over the bar with the goal at her mercy.
Town threatened again just before half time, as Erica Byron’s cross was knocked down by Remi Bains and Summerfield saw her efford blocked.
The second period was a very hotly contested, open affair, as Aurora Ryan was inches away from giving Town the lead, her shot trickling just wide.
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Some excellent defending from Millie Guest then allowed Jess McKay to burst down the wing and put in a cross that was deflected against the post.
With Carroll and Lisa Nixon controlling the midfield, plus Rachel Kosky’s fine performance, Luton remained on top, Ryan and McKay forcing the keeper to save well, while Carroll’s free kick cannoned off the bar.
Stevenage then started to get into the game more, forcing Hatters keeper Kezia Hassall into action.
The visitors grabbed the all-important goal with just 15 minutes to go, with a header from a corner.
Luton tried to snatch a last-gasp equaliser, but despite sending several decent deliveries into their opponents’ penalty area, Stevenage came out on top.
Town remain bottom of the table with just eight points from 14 games.
They visit eighth-placed Ipswich Town on Saturday and then host second from bottom Denham United on Monday evening.