Substitute Jason Scotland ultimately proved to be the match winner for the relegation-threatened Tykes with his third goal in as many games.
Earlier, Jim O'Brien had given the away side the lead, which was cancelled before Mustapha Carayol and Curtis Main swung the game in Middlesbrough's favour and Scott Golbourne levelled matters again.
Only goal difference keeps Barnsley in the relegation places, and Flitcroft was quick to warn his players against complacency.
"It's got to be 46 games and this group of players will not get carried away," he said. "I won't let this group of players get away with anything; that's my job as the manager.
"I don't do people who come to work to be average - I do people who come to work to achieve, whoever that person is.
"The game had everything. Like any great rollercoaster it had a bit of everything in it. Every player played a massive part in that win - that's a special group of players in there.
"This group of players are achieving their potential week in, week out, and that's all I ask. If you give everything you've got you hit the levels of perfection that I talk about to these players.
"I'm telling this group to become heroes and achieve something that at one stage looked impossible and gets talked about for years to come."
Flitcroft also praised former Barnsley boss Keith Hill, who was sacked in December with the side bottom of the table and four points adrift of safety.
"Keith Hill's assembled an incredible squad - his recruitment is amongst the best in the country," added Flitcroft. "Fortunately now we're getting the best out of them.
"We've played well all season, and I'll stress that to anyone who wants to listen."