Talk of a top-four challenge followed the recent upturn in fortunes at Old Trafford, but Albion ensured a key week would start with a loss for the visitors.
Mata's foolish sending-off midway through the first half gave Tony Pulis' men an advantage they capitalised on, with Rondon's fine finish earning a 1-0 victory that almost certainly secures his side's survival.
The Venezuela striker's fourth goal in six Premier League matches condemned United to a first league defeat at The Hawthorns since March 1984 and saw them fall behind in the race for the Champions League.
magista gray West Brom were perhaps unfortunate not to take the lead in a first half which saw Mata pick up the first red card of his club career - and United's first sending-off of the season - after collecting two bookings in less than three minutes.
mercurial cr7 gold Van Gaal's men showed signs of recovery as they returned from half-time brightly, only for Rondon to lash home and end Albion's run of 11 winless league fixtures at home to the Reds.
Defeat leaves United three points off rivals Manchester City - who also boast a game in hand - and seemed a distinct possibility after a lacklustre opening period.
Anthony Martial's tame effort after two minutes was all Van Gaal's side could muster, whereas the hosts proved a threat from the outset.
Rondon's directness made him a nuisance but it was his vision that almost undid United, with his clipped ball to Craig Dawson headed wide in the ninth minute.
nike soccer cleats pro Saido Berahino's scuffed attempt from a clever Craig Gardner header was blocked by the returning Chris Smalling as the home side continued to press, with the natives unhappy to see Daley Blind's high foot on Berahino adjudged to have taken place outside the box.
The noise inside the Hawthorns rose several notches with that decision and - shortly after Gareth McAuley headed inches wide, unaware the offside flag was raised - it went up further.
Less than three minutes after being booked for encroaching on a quickly-taken free-kick, Mata's wild swing at former team-mate Darren Fletcher led to a second yellow.
It naturally led pressure to mount on United's backline, but the closest Albion came before half-time was an audacious half-volley from the unlikely source of Dawson.
Van Gaal's men attempted to capitalise on those missed opportunities as they returned from the break brightly.
Marcus Rashford was largely anonymous but saw a snapshot deflect wide after exceptional work down the left by Martial.
Jesse Lingard was the next to threaten, cutting back and curling a strike just over from the edge of the box.
Ander Herrera hit a free-kick into the wall as United continued to threaten a West Brom defence destabilised by McAuley limping off, only for replacement Sebastien Pocognoli to create the opener.
tiempo legend v white After referee Mike Dean waved play on, the ball was played out wide for the Belgian full-back to fizz in a cross that Rondon controlled well and fired home sweetly.
superfly 100 It was a 66th-minute lead that United rarely threatened to cancel out, with the introduction of Memphis Depay in place of 18-year-old Rashford failing to jump-start the visitors.
Most of the play was in their half but, like the visitors, Albion were unable to create any clear-cut chances - not that it mattered in the end.
