In the final minute of an entertaining encounter United defender Darren Dods pulled down Giovani dos Santos, allowing the former Arsenal player - on as a second-half substitute - the opportunity to score from the spot.
United's debutant keeper Grzegorz Szamotulski saved the first effort but Henry followed up to knock the ball into the net.
"We have seen that he is an intelligent player and we have seen some good passes," Rijkaard said after the match.
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"We have to take into account he has not played for a long time and it was his decision to go and play. He played well."
It could have been different if Barry Robson's 82nd-minute header had not been chalked off for a push on Barca defender Eric Abidal and if Lee Wilkie's last-minute header had not been headed off the line by Juliano Belletti, but in the end the classier side won through.
United gave a debut to 'keeper Szamotulski, the former Sturm Graz player who signed yesterday, and he was kept busy in a relatively entertaining first half.
The visitors quickly took control of the game and in the 14th minute Santiago Ezquerro casually swept a Xavi cross over the bar from eight yards out when more focus might have brought the opener.
Three minutes later, Dundee United midfielder Morgaro Gomis fouled Ronaldinho 25 yards from goal and the Brazilian flashed his right-footed free-kick off the outside of the post.
Despite playing in second gear at times, Barca continued to dictate the tempo and in the 28th minute Ezquerro drew a good save from Szamotulski with a drive from distance.
Samuel Eto'o made a hash of a great chance set up by Andres Iniesta before driving straight at Szamotulski from close range after taking a clever Ronaldinho pass.
In between those two chances Xavi volleyed Ronaldinho's cross past the post from the edge of the box and Ezquerro fired wide with only the United keeper to beat.
Barca made seven changes at the break and just 25 seconds in to his debut, Henry, on for Eto'o, whipped a shot inches past the post from the edge of the box.
United's overly-enthusiastic defender Lee Wilkie was then booked for a foul from behind on Henry to the jeers of the Tannadice crowd.
The Catalan giants appeared to be trying to walk the ball into the net and in another attack that left United threadbare at the back, Henry curled his right-footed shot from just inside the box high and wide.
In the 80th minute Barcelona substitute Bojan Krkic went through on goal but hesitated with only Szamotulski to beat, allowing the Tannadice 'keeper to save at his feet.
In the 82nd minute United skipper Robson headed Steven Robb's cross in off the post but the cheers soon died down when the goal was chalked off for a push on Eric Abidal.
Then came the drama of Henry's debut goal and Wilkie's near miss.