The Swans fell out of the top six for the first time since the opening day when they lost 2-1 to Middlesbrough in midweek.
The Welsh side conceded a goal either side of half time at the Riverside Stadium before Yan Dhanda's first goal of the season in the 78th minute proved only to be a consolation.
It was only the third time Swansea have been beaten this season and meant that they slipped to seventh in the table on a night when victory would have taken them top.
They are still only two points behind league leaders Norwich City and have a better goal difference than the Canaries.
Steve Cooper will be pleased to now return to the more familiar surroundings of the Liberty Stadium, as no team in the Championship has let in fewer goals at home this season than Swansea (four).
Opponents Luton may simply be focused on not conceding themselves, as their last trip to South Wales only a week ago ended in disaster as they were thrashed 4-0 by Cardiff City.
The win took them up to 11th and four points away from the playoffs, so they may see Saturday's game as an opportunity to cut that gap even further.
Aside from their defeat at the Cardiff City Stadium, Luton's away record is good – they have picked up 20 points from a possible 33 on the road since Nathan Jones returned to the club.
Three of those points were earned in a 1-0 win at the Liberty Stadium at the end of June, the 11th successive game between these two sides that has not ended in a draw.
Swansea City Championship form: DLWDWL
Luton Town Championship form: WDDDLW
Yan Dhanda could come into the Swansea starting lineup following his goal as a substitute in midweek, while Matt Grimes is also pushing for a start.
Jamal Lowe has not scored in his last eight games and was brought off at half time against Middlesbrough, so could be replaced by Viktor Gyokeres.
Luton's Martin Cranie was forced off through injury just before half time against Norwich, and James Bree is likely to replace him on Saturday.
Swansea City possible starting lineup:
Woodman; Cabango, Bennett, Guehi; Roberts, Smith, Grimes, Manning; Dhanda; Gyokeres, Ayew
Luton Town possible starting lineup:
Shea; Bree, Lockyer, Pearson, Norrington-Davies; Rea; Clark, Berry, Dewsbury-Hall, Moncur; Collins
We say: Swansea City 1-0 Luton Town
Luton will be full of confidence after beating the league leaders, but a trip to Swansea is undoubtedly a tough one. The Swans are unlikely to have as much joy in front of goal against the Hatters as their South Wales neighbours did, but we are still backing them to come out on top.