Mourinho is desperate to restore his tarnished reputation after being sacked by Chelsea last season and the United manager enjoyed an encouraging return to the touchline in his first league match since a December defeat at Leicester triggered his exit from Stamford Bridge.
In the absence of Paul Pogba, their world record signing, United eased to victory after Mata punished a horrible mistake by Bournemouth defender Simon Francis just before half-time and Rooney added the second after the interval.
That set the stage for the latest memorable moment in Ibrahimovic’s glittering career as the Swedish forward netted with a fine strike to mark his Premier League debut in the same goalscoring style he celebrated his maiden appearances in Serie A, La Liga, Ligue 1 and the Champions League.
After a lackadaisical first half, United moved smoothly through the gears once Mata opened the scoring and, although Adam Smith got one back for Bournemouth, Mourinho will hope to build on the momentum from this result as he eyes a title challenge.
Bournemouth were United’s opponents when they concluded a frustrating league campaign last season, but whereas the staid atmosphere at Old Trafford that day reflected the drab nature of Louis van Gaal’s reign, there was a whiff of revolution in the air on the genteel south coast as Mourinho’s reign got underway.
Mourinho has wasted little time stamping his authority on an underachieving squad and, although world record signing Pogba was serving a one-man ban incurred at Juventus last season, the United boss paraded new signings Ibrahimovic and Eric Bailly.
Ibrahimovic started as United’s central striker with Rooney behind him and the wide roles filled by Anthony Martial and Mata, who featured despite the Spaniard’s touchline spat with Mourinho when he was substituted having only just come on in last weekend’s Community Shield win over Leicester.
Mourinho’s men took 23 minutes to muster a shot and even then Martial’s effort from the left side of the penalty area flew well wide of Artur Boruc’s goal.
Disastrous
But United finally pieced together an incisive attack when Ander Herrera picked out Antonio Valencia and the right-back crossed to Mata, who set up Rooney for a low shot straight at Boruc.
Apart from a few nice moments from Bournemouth winger Jordon Ibe, making his debut after joining from Liverpool, this was soporific stuff in the sunshine.
Out of nowhere, United were gifted the breakthrough five minutes before half-time after a disastrous mistake by Francis.
Mata scampered after Herrera’s long pass and Francis responded with a panicked and under-hit backpass that the Spaniard seized on.
Boruc was able to save Mata’s first shot, yet United’s luck was in as the ball hit Francis, rebounding in Mata’s path for the winger to tap into the empty net.
Ibrahimovic had been anonymous in the first half, but he came to life after the interval, unfurling a typically extravagant volleyed backheel that sent Rooney clear for a shot saved by Boruc.
United were forcing the issue more now and Rooney deservedly doubled their lead with a close-range header after Valencia’s cross was miscued into his path by Martial.
Meanwhile, goals early in the second half from Adam Lallana, Coutinho and Sadio Mane put Jurgen Klopp’s Liverpool 4-1 up, but efforts from Alex Oxlade-Chamberlain and Calum Chambers made for a nervy finish.
It was only Liverpool’s second win at Arsenal in 21 attempts and put an early dent in Arsene Wenger’s hopes of leading the London club to a first league title since 2004.
The Frenchman, who celebrates his 20th anniversary as Arsenal manager in October, has now seen his team beaten at home in their opening league game three times in four years.
Klopp, starting his first full season as Liverpool manager, celebrated each of the visitors’ goals with trademark abandon, but he will have been concerned by an injury that forced Coutinho off.
Injuries to Per Mertesacker and Gabriel, plus Laurent Koscielny’s lack of match fitness, forced Wenger to deploy 21-year-old Chambers and 20-year-old new boy Rob Holding at centre-back.
Liverpool, meanwhile, boasted some 63 million pounds ($81.5 million, 73 million euros) of new players in Mane, Georginio Wijnaldum and Ragnar Klavan.
But after some untidy opening exchanges, Arsenal were first to impose themselves on the game.
Aaron Ramsey, playing in a number 10 role, had a couple of sights of goal, jabbing a shot straight at visiting goalkeeper Mignolet and then lifting an ambitious lob well over the bar.
Liverpool left-back Alberto Moreno was proving a typically chaotic presence and on the half-hour his untidy, full-blooded challenge on Walcott gifted Arsenal a penalty.
Walcott took the spot-kick himself and saw Mignolet plunge to his right to push it away.
– Mane’s Klopp piggyback –
But barely a minute later the England forward atoned as Alex Iwobi’s pass caught Moreno out of position and Walcott clipped a low shot inside the left-hand post.
Stung, Liverpool responded, Wijnaldum seeing a side-foot effort saved by Petr Cech, and in first-half stoppage time Coutinho netted the equaliser in memorable fashion.
Having won a free-kick by going down a little easily under pressure from Holding, the Brazilian took charge of the set-piece himself, curling an exquisite 25-yard shot right into the top-left corner.
It had been an evenly balanced first half, but within 18 minutes of kick-off in the second Liverpool had the game in the bag thanks to three delightful goals.
Four minutes in, Coutinho sent Wijnaldum scampering towards the byline on the left with a stabbed first-time pass.
The former Newcastle United midfielder cut inside and lifted a cross to the back post, where Lallana chested the ball down before steering it past the outrushing Mignolet.
Seven minutes later, an attack from the opposite flank produced the same result, Nathanie Clyne crossing from the right and Coutinho darting in at the near post to volley home.
Mane opened his Liverpool account in the 63rd minute with a splendid goal, driving down the right and slipping between Chambers and Nacho Monreal before hammering a left-foot shot past Mignolet.
The Senegal international celebrated by leaping onto Klopp’s back. -AFP.
