City went ahead inside the opening two minutes through Danny Haynes, but goals from Hugo Colace and Daniel Bogdanovic put the Tykes ahead.
And after Nicky Maynard scored either side of the break to put the hosts ahead, further goals from Haynes and Paul Hartley extended their lead, meaning Andy Gray's header was nothing more than a consolation.
The win moves the Robins above Barnsley in the table and effectively ends any fears of relegation, while the Tykes must now contemplate a mid-table finish as they lose touch with the top six places.
Millen will have been keen for his side to build on their impressive performance against Newcastle and he could not have hoped for a better start as they went ahead after 69 seconds.
Marvin Elliott advanced down the right and whipped in a cross for Haynes, who powered a header past Luke Steele.
But, in a frantic start to proceedings, Barnsley levelled just a minute later.
Luke Potter found space on the left and produced a fine cross for Colace at the back post and the Argentinian fired home.
The visitors began to take control and the impressive Bogdanovic had a great chance to give his side the lead in the 20th minute, but his close-range header was saved by Gerken.
But the Maltese striker made amends for his wastefulness just five minutes later when he did put his side ahead and it came straight off the training ground.
Bobby Hassell took a free-kick from the right and instead of whipping a ball into the box, he cut the ball back to Bogdanovic, who had peeled off from his marker and drilled into the bottom corner.
Barnsley were in control of the game, but just as it looked as though they would head into the half-time interval in the lead, City hit back - and former Tykes winger Jamal Campbell-Ryce was inevitably the architect.
The tricky wideman beat right-back Hassell and got to the byline, before cutting back to Maynard, who nodded in from five yards.
The hosts carried the momentum into the second period and took the lead in the 56th minute.
Full-back Bradley Orr broke into the penalty area and crossed for Maynard, who ghosted in at the pack post and finished with a stooping header for his 16th of the season.
And Maynard turned provider as Millen's men forged further ahead seven minutes later when he set up Haynes to convert from close range for his second of the evening.
Things got even better with 14 minutes left when Ryan Shotton was adjudged to foul Maynard inside the area and Hartley stepped up to convert the spot-kick.
Barnsley brought some respectability to the scoreline when Gray finished off a superb move by heading in Colace's cross with nine minutes left, but there was to be no comeback.