United included record signing Angel di Maria in their starting line-up, but rarely looked like scoring at Turf Moor as Burnley picked up a first point since returning to the top flight.
Former United youngster David Jones almost gave Burnley a third-minute lead when the midfielder curled a 25-yard free-kick against the crossbar, with David de Gea rooted to the spot.
Another ex-Red Devil then kept the scores level as Burnley goalkeeper Tom Heaton produced a fine reaction stop on 15 minutes to keep out Robin van Persie’s well-struck shot.
New boy Di Maria was one of the few bright sparks for United on his debut as chances were at a premium before Van Persie saw a second-half effort blocked on the line by Dean Marney.
Di Maria was replaced with 20 minutes to go after appearing to take a kick to his calf and Wayne Rooney headed wide at the far post from a corner.
United appealed for a penalty late on when a shot from Ashley Young, who also appealed in vain for a spot-kick in the first half, clattered into Ashley Barnes, but Van Gaal’s side had never looked like getting their season up and running following previous setbacks against Swansea and Sunderland.
Di Maria, playing in a midfield three alongside Juan Mata and a slightly deeper Darren Fletcher, received a hero's welcome from the away fans as he took to the pitch, but he was marginalised early on as Burnley took control from the off.
With less than three minutes gone, United handed the hosts a good chance to score and they almost took it when Phil Jones barged over Lukas Jutkiewicz to earn a free-kick right on the edge of the box.
David Jones beat De Gea with a curling effort from the resulting set-piece, but the ball struck the bar and bounced out to safety.
Soon after Burnley were gifted their second opportunity when Jonny Evans, in an almost identical error to the one he committed at MK Dons on Tuesday, sold De Gea short with a backpass, but the Spaniard came out to block Jutkiewicz's shot.
Di Maria then produced his first bit of magic to spark United into life. The Argentinian lofted a 40-yard ball over the top of the home defence and Van Persie cushioned the ball perfectly on his chest, but his volley was well saved by Heaton
De Gea was called into action again, racing out of his box to clear just in time after a defensive mix-up before he parried a swirling volley from Jones shortly after watching Scott Arfield head over from close range.
Any hopes of a United goal seemed to rest on Di Maria's shoulders. The former Real Madrid midfielder kept the Burnley back four on their toes with his pace and trickery on the attack and he was also proving effective from deep.
Di Maria picked out Rooney with another long diagonal ball. The United and England captain prodded the ball to Van Persie, but Jason Shackell intervened.
Fletcher, looking increasingly isolated in midfield, was booked for tugging Danny Ings' shirt.
United started to come into the game a bit more towards the end of the first half and Young went down in the box under pressure from Kieran Trippier, but Chris Foy waved play on.
After a dull opening five minutes of the second half, United created a couple of good chances, but once again they could not find the net.
Marney saved Van Persie's shot on the line after a good run from Di Maria and the Dutchman spurned another chance soon after by heading Fletcher's chipped pass onto the roof of the net.
Then came a sight no United fan wanted to see - Di Maria down on the floor holding his right leg. The player got back to his feet after treatment, but moments later Van Gaal took his record signing off and replaced him with Anderson.
Van Persie was then replaced by Danny Welbeck up front.
United's lack of concentration at the back remained Van Gaal's biggest worry, as Antonio Valencia carelessly played the ball straight to the unmarked Arfield on the edge of his own box, but he failed to beat De Gea.
At the other end Mata, who was having a day to forget, ploughed the ball high and wide before the Spaniard came off for Adnan Januzaj with four minutes to go.
In the dying stages United thought they should have had a penalty when Young's shot appeared to hit Barnes' arm, but Foy was not interested and the game petered out into a draw.