Pre-match media reports suggested Van Gaal was one defeat away from the sack and the 64-year-old Dutchman saw his team's run of games without a win extended to seven at a windswept Britannia Stadium.
A weak back header from Memphis Depay enabled Glen Johnson to tee up Bojan Krkic for Stoke's opener in the 19th minute and Marko Arnautovic brilliantly slammed home the hosts' second goal seven minutes later after Bojan's free-kick hit the wall.
It is United's worst run of results since an eight-game winless streak between December 1989 and January 1990, which could cost Van Gaal his job 18 months after his appointment as the successor to David Moyes.
Van Gaal on the ropes, Hiddink comes out swinging
Van Gaal, who dropped Wayne Rooney to the bench, had described the fixture as "must-win", having stormed out of his pre-match media conference due to the speculation about his future.
In the last month United have slipped out of the Premier League's top four and been eliminated from the Champions League in the group phase following a 3-2 defeat at German side Wolfsburg.
They were knocked out of the League Cup by second-tier Middlesbrough in October.
United face Chelsea at Old Trafford on Monday and the defeat at Stoke is likely to fuel speculation that the 20-time English champions will turn to Jose Mourinho, who was sacked by Chelsea last week.
Man Utd players fighting for Van Gaal – Rooney
While Stoke, managed by former United striker Mark Hughes, teased and tormented the visitors on the pitch, the home fans goaded Van Gaal with chants of "Jose Mourinho!" as the game wound down.
Van Gaal was rooted to his dug-out seat throughout the 90 minutes and looked a shell-shocked figure as he walked away at the final whistle, pausing briefly to wave to the travelling supporters.
Stoke took the game to United from the off, with Xherdan Shaqiri and Arnautovic causing particular problems.
Depay's blunder enabled Stoke to go ahead, with Johnson seizing on the Dutch winger's disastrous header and squaring for Bojan, who threaded a shot through the legs of United defender Phil Jones on the line.
Embattled Van Gaal storms out of United press conference
Stoke's second goal was a spectacular long-range strike from the right boot of Arnautovic.
When Bojan's free-kick cannoned against the United wall, it broke for the enigmatic Austrian, who produced a 20-yard thunderbolt for his sixth goal of the season.
Arnautovic then had a wonderful chance to put the game out of United's reach when he broke the offside trap in latching onto Bojan's astute pass, but with only David de Gea to beat, he dragged his shot wide.
It was no surprise that Van Gaal acted at half-time by bringing on Rooney for the ineffective Depay.
Rooney must have thought he had thrown his side a lifeline when he cut the ball back for the unmarked Marouane Fellaini, but from eight yards out the Belgian was thwarted by a one-handed save from Stoke goalkeeper Jack Butland.
Although Stoke failed to hit the heights of their first-half display, they continued to look the more threatening going forwards, with De Gea making crucial saves to prevent both Arnautovic and Bojan getting on the scoresheet again.
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