Swansea are just one point off the playoffs with eight games to go, while Luton are within five points of safety heading into the final straight.
The Swans laid down a real marker in their first game back following the three-month layoff by cruising to a 3-0 win over Middlesbrough, a result that cost opposition boss Jonathan Woodgate his job.
Steve Cooper's side have lost just one of their last seven league matches, but four of those have ended in draws, meaning that there is still a three-place gap on the top six.
While the Welsh outfit are looking up at the sides above them, the same is even more true of Luton, who are rock bottom of the division.
Saturday's 1-1 draw with promotion-chasing Preston North End is a good result on the face of it, especially having trailed until the 87th minute, but there is still a five-point margin on Middlesbrough in 21st.
That was Town's third draw in a row, after they also held Stoke City and Wigan Athletic before the hiatus, and Jones will be looking to take the positives from those performances.
It has been a tough campaign for Luton on their travels, though, taking just four points from their last 14 away Championship matches.
Swansea, by comparison, have lost only one of their last nine home Championship games (W4 D4) - a 3-2 defeat to Derby County in February.
The Swans also boast an impressive record against Saturday's opponents, winning their last three league meetings without conceding a single goal.
Indeed, Luton have won just one of their last 13 away league visits to Swansea, although their most recent encounter at the Liberty Stadium came in February 2008.
Swansea's Championship form: DWLDDW
Luton's Championship form: WLWDDD
Central defender Mike van der Hoorn is still recovering from injury for Swansea and will sit out this match.
Cooper otherwise has a fully-fit squad to choose from, but changes are expected to be kept to a minimum.
As for Luton, Callum McManaman scored their late leveller against Preston and may therefore have done enough to warrant inclusion from the off against Swansea.
Swansea possible starting lineup:
Woodman; Naughton, Cabango, Wilmot, Bidwell; Byers, Grimes; Kalulu, Gallagher, Ayew; Brewster
Luton possible starting lineup:
Sluga; Bree, Carter-Vickers, Pearson, Potts; Rea, Mpanzu, Tunnicliffe; McManaman; Cornick, Collins
We say: Swansea 2-1 Luton
Jones has lost none of his last 13 league matches in charge of Luton and has already beaten Swansea away once this season with Stoke in October. However, Town have won just one of their last five games and are bottom of the table for a reason, so we are going for a home win on Saturday.