Frustrated Blades fans were staring a fifth successive defeat in the face when Henderson grabbed the lifeline of a penalty seven minutes from the end.
It was his second from the spot after his earlier leveller had cancelled out Barnsley's opener.
United keeper Ian Bennett produced a pair of impressive saves to deny Barnsley as the Oakwell side threatened to claim an early advantage.
When Barnsley hunted for the opener, again Bennett was in defiant mood. He held onto a dangerous header from Franca Anderson Silva and then made a great stop when Daniel Bogdanovic volleyed from 20 yards.
Barnsley's Argentinian midfielder Hugo Colace found a gap midway through the first half but Bennett made a superb point-black stop to turn away his shot.
United struggled to produce an early threat but Ched Evans flashed a stinging shot wide from 20 yards after a smart turn and, when Henderson headed goalwards, Ryan Shotton intervened.
United were hampered when keeper Bennett was substituted at half-time with a hand injury to be replaced by Mark Bunn.
Barnsley finally produced the breakthrough in impressive style after 53 minutes when Brazilian Silva latched onto a half-cleared throw in and smashed in a terrific angled shot from 20 yards.
Two minutes later the visitors came within a whisker of levelling when Keith Treacy raced into the Barnsley area but his rasping left-foot drive hit the post.
On 59 minutes United were level when Evans went down in the area as keeper Luke Steele dived at his feet and Henderson crashed home the spot-kick in emphatic style.
Barnsley reclaimed the lead after 74 minutes when Jon Macken's superb low cross from the right was forced over the line by Bogdanovic.
But Henderson slotted home his second penalty on 83 minutes after Carl Dickinson had brought down James Harper in the box.