The hosts picked up a narrow 1-0 victory over Coventry City on Saturday after a draw to begin the season, while their visitors' winning start was followed by a 3-2 defeat to promotion-chasing West Bromwich Albion.
After narrowly escaping relegation to League One in the 2019-20 campaign, Valerien Ismael guided Barnsley to the playoffs against the odds last season.
The Tykes collected an eye-catching points tally of 78 to pip the likes of AFC Bournemouth and Reading to fifth spot in just their second season back in the second tier after promotion from League One.
That finish saw them handed a tie with Swansea City in the playoff semi-finals, and a 1-0 home defeat in the first leg meant they faced a very tough test upon their trip to South Wales.
While they were unable to overcome the deficit, eventually drawing 1-1 on the day and losing 2-1 on aggregate, the South Yorkshire outfit did give an impressive account of themselves, but they will now start a new chapter under the management of Markus Schopp after the departure of Ismael to West Bromwich Albion over the summer.
The Austrian kicked off his tenure with an impressive point following a 1-1 draw away against Cardiff City, as Toby Sibbick drew them level in the 69th minute after Marlon Pack's opener for the Bluebirds.
After losing on a penalty shootout to Bolton Wanderers in the first round of the EFL Cup after a goalless draw, the Tykes returned to league action last time out, and it did not take them long to record their first Championship win under Schopp.
In their bid to record back-to-back league victories, they take on a Luton Town side who will be keen to bounce back from a defeat to West Bromwich Albion.
In their visit to promotion-chasing West Brom, Nathan Jones's men went three goals behind as Callum Robinson and Karlan Grant got on the scoresheet after Kal Naismith's early own goal, and the result looked all but sealed.
Nonetheless, the Hatters certainly showed what they were capable of under Jones against one of the league's strongest sides, after starting the season with a resounding 3-0 victory over Peterborough United.
Elijah Adebayo put them ahead on the half-hour mark, and that one-goal lead lasted deep into the second half until Cornick doubled their advantage and Fred Onyedinma immediately made it three in the 71st minute.
Following Jones's return to the club after previously guiding them to promotion back to the second tier, the only way seems to be up for the Hatters, as they look to again improve this campaign after last season's commendable 11th-placed finish.
Barnsley will likely remain without centre-back Mads Andersen, who is battling a knee injury, with Liam Kitching expected to keep his spot in the back three alongside Michal Helik and Toby Sibbick in his absence.
The Tykes faced a huge loss in the summer as midfielder and captain Alex Mowatt departed at the end of his contract to join former manager Valerien Ismael at West Bromwich Albion.
That has triggered the movement of talented 21-year-old Callum Styles into the centre, after hugely impressing in a left wing-back role previously.
In the face of those defensive absences, Jones had to deploy a somewhat makeshift back four for the visit to the Hawthorns, with utility man Kal Naismith partnering with Gabriel Osho, flanked by James Bree and Amari'i Bell in the full-back spots.
The front three of Fred Onyedinma, Elijah Adebayo and Harry Cornick should remain unchanged, with all three having found the net in the opening game of the season, while Cornick was again on the scoresheet last time out.
Onyedinma particularly impressed in that opening win over Peterborough, as he scored the third goal and assisted the other two on his debut after joining from Wycombe Wanderers in the summer, offering Nathan Jones an exciting new option going forward.
Barnsley possible starting lineup:
Collins; Sibbick, Helik, Kitching; Brittain, Styles, Palmer, Williams; Morris, Woodrow, Frieser
Luton Town possible starting lineup:
Sluga; Bree, Osho, Naismith, Bell; Clark, Campbell, Ruddock; Cornick, Adebayo, Onyedinma
We say: Barnsley 1-1 Luton Town
Both sides have shown a general upwards trajectory in recent years and have kicked off the new season in impressive fashion, making this a particularly exciting and unpredictable encounter.
On this occasion, we cannot quite split them, and are opting for a hard-fought point for each side in what should be an end-to-end encounter.