From the high of March’s Champions League comeback win at Paris St Germain to chastening losses to the likes of Everton, Newcastle and Watford, this will be remembered as challenging year of transition at Old Trafford.
There remains plenty of work to do but United head into the New Year buoyed by back-to-back wins, with Martial and Rashford scoring at Burnley just 50 hours after the comprehensive comeback against Newcastle.
Solskjaer’s side could have scored more at Turf Moor but this was another victory when bossing possession, while they also ended a club-record 14-match run without a Premier League clean sheet.
Burnley have not beaten United since 2009 and never looked likely to spring a surprise on Saturday, with Rashford hitting a post in a first half that Martial opened the scoring in after Charlie Taylor flapped under pressure.
Phil Bardsley forced David De Gea into a fine save after the break, but Sean Dyche’s men looked more likely to get a red card than a goal on a night when Rashford turned home at the death to add gloss to the scoreline.
The big talking point ahead of kick-off was the absence from the squad of Paul Pogba, who had been expected to start after two substitute appearances following an ankle injury.
United made four alterations and Burnley made two at Turf Moor, where the home side looked to have been impacted most by their Boxing Day exertions.
Returning Ashley Barnes’ wayward effort late in the opening period was the best they could muster before the break, although Jack Cork nearly met a James Tarkowski header across goal midway through the first half.
United broke from that opportunity and Rashford hit the outside of a post, with the in-form forward continuing to look confident as he took free-kicks and played with directness.
Martial was not as sharp early on but grew into proceedings.
United youth graduate Bardsley cleared off the line as the Frenchman took aim from close range, with Brandon Williams, impressing at left-back, nearly finding the striker as Burnley goalkeeper Nick Pope called for attention.
The England international was able to continue after several minutes of treatment and was soon picking the ball out of his net.
Martial was the scorer but Andreas Pereira’s pressure was key.
The Brazil midfielder forced a mistake out of full-back Taylor and played a lovely ball in for the forward to coolly tuck home with 44 minutes on the clock.
Martial found the net again within minutes of the second half starting, only for the goal to be ruled out by referee Mike Dean for his foul on Tarkowski.
Pope also denied the Frenchman with his feet, but Burnley were pushing higher up the field and having more attempts after their half-time pep talk. But the home side’s decision-making was as poor as their finishing.
Ben Mee looked fortunate to get away with a booking for a challenge on Daniel James as the match entered the final 30 minutes. Taylor soon joined him in the notebook for a foul on the Welsh flyer.
For Burnley’s fight at the back, there were few signs of life at the other end. Bardsley went closest to an equaliser, with his fizzing strike bound for the bottom corner before De Gea’s low save in the 69th minute.
Substitute Johann Berg Gudmundsson curled a free-kick over and Martial hesitated when it looked likely he would wrap up the game.
Burnley desperately pushed for a leveller and would be caught deep in stoppage time on the counter, with Rashford rounding Pope and prodding home from the floor in front of the travelling support.