The Tigers were already two goals down by the time substitute Lewis-Potter headed in from close range, and Barnsley went on to complete their win with a third goal in added time.
With Josh Magennis absent, George Honeyman came into the side in the only change to the starting eleven following the midweek hammering of Preston North End. With Kevin Stewart also missing from the squad through injury, Stephen Kingsley and Leonardo Da Silva Lopes came onto the bench.
On a chilly afternoon in South Yorkshire the Tigers had a couple of promising moments early on as Kamil Grosicki attacked down left, while the hosts had a first shot in anger when Cauley Woodrow fired over from 20 yards in the fifth minute.
Most of the early pressure was coming from the away side, resulting in a number of corners that Barnsley were managing to deal with.
However, it was Barnsley who took the lead midway through the half. A cross from the home side’s left was cleared to the edge of the box where Alex Mowatt curled a lovely shot past George Long.
Barnsley appealed loudly for a penalty shortly after when the ball appeared to strike Reece Burke’s arm inside the box but the referee waved play on.
The Tigers’ first real chance came four minutes before the break when a lucky deflection had Jarrod Bowen through on goal but, although he managed to beat goalkeeper Sami Radlinger with a shot, the ball rolled agonisingly wide of the far post.
Long turned Mowatt’s free kick wide in the final minute of the half as the host’s went into the interval with a one-goal lead.
McCann made a double change at the break with Da Silva and Tom Eaves replacing Daniel Batty and Honeyman.
The Tigers looked a little more lively at the start of the second half, although Barnsley thought they had doubled their lead when Conor Chaplin bundled the ball in from close range before seeing that the offside flag had been raised.
Reece Burke picked up a booking for a foul just inside his own half before Jackson Irvine sent a shot just wide after being set up by Eaves.
A second Barnsley goal arrived 15 minutes from time. The ball was worked through for Mike Bahre and he beat Long with a composed finish.
That prompted a final change by the Tigers as Lewis-Potter replaced Callum Elder.
And it was Lewis-Potter who pulled a goal back for visitors nine minutes from time. Grosicki’s cross to the far post was nodded back by Eaves for the Academy product to head in from close range for the first goal of his senior career.
Josh Bowler saw an effort deflected wide as the game entered added time, but with the Tigers throwing men forward they were caught out as Chaplin made it 3-1 with was pretty much the last kick of the game to seal Barnsley’s first win since the opening day of the season.
Barnsley: Sami Radlinger, Jordan Williams, Ben Williams, Bambo Diaby, Mads Andersen, Jacob Brown, Cauley Woodrow (Patrick Schmidt 88), Mike Bahre (Luke Thomas 82), Conor Chaplin, Aapo Halme, Alex Mowatt.
Subs Not Used: Brad Collins, Kenny Dougall, Toby Sibbick, Clarke Odour, Mamadou Thiam.
Hull City: George Long; Eric Lichaj ©, Reece Burke, Jordy de Wijs, Callum Elder (Keane Lewis-Potter 76); Daniel Batty (Tom Eaves 46), Jackson Irvine, George Honeyman (Leonardo Da Silva Lopes 46); Josh Bowler, Kamil Grosicki, Jarrod Bowen.
Subs Not Used: Matt Ingram, Ryan Tafazolli, Stephen Kingsley, Matthew Pennington.
Referee: Mr J. Brooks.
Attendance: 13,598 (1,941 Visiting Supporters).