Manchester United are ensuring Manchester City, seeking a third title in four years, feel some breath on their necks. This victory closes the gap to eight points and eyes now turn to Wednesday when Pep Guardiola’s side are at Aston Villa. With six games left the chance remains remote that City will perform a Devon Loch but at this juncture United are the same margin behind after 32 matches as in April 2012 when the roles were reversed and Roberto Mancini’s side took the title on the final day, courtesy of Sergio Agüero’s 94th-minute winner against QPR. That run-in included a Manchester derby – the definition of a six-pointer. For this year’s slim chance to keep dreaming United have to thank Mason Greenwood and Edinson Cavani, whose goals on 83 and 90 minutes sealed a late win. Ole Gunnar Solskjær said: “It is probably unrealistic [to catch City] but stranger things have happened in football. We just have to do our job. We’ve always said this year has to be progress and improvement, we’ve got as many points as last season [at the end] and if we get more we’ve got more: that’s progress. We want to finish with a trophy in the Europa League, we’ve got loads of games and loads to focus on.” Greenwood “was fantastic”, the manager said. “Two very good goals coming in off the left. He’s mixing up his game. He goes inside and outside, he’s maturing all the time. It’s lovely to see. He’s put the work in on the training ground and reaps the rewards. Last season he was young, now he’s had almost two seasons in the first team. “Especially in the last three or four months I’ve seen how mature he is on the training ground and he plays with maturity and understanding. He’s very creative but plays simple when he has to.” In the first half Burnley had been as attritional as any brochure for Sean Dyche’s side might say. Yet though United were slicker the visitors also moved forward with a pace and control that are not always associated with them. In Chris Wood they had a No 9 who was hunting for a third goal in three visits here and he gave Dean Henderson a fright with the clock not yet at 20 seconds in a clownish moment for United’s No 1. Matthew Lowton launched a long diagonal ball from his own half and Henderson ran 10 yards from his line to punch clear, only to be beaten by Wood, who headed in. The effort was ruled offside so Henderson escaped but it was no way to calm his defence. Solskjær said: “That is a wake-up call for him, he’s a proactive keeper and Dean is still learning and maturing.” Marcus Rashford – excellent throughout – was making runs in behind that Luke Shaw and Greenwood saw either too late or not at all. One of these missed opportunities prompted a loud expletive from the No 10. Burnley, buoyed by Arsenal’s late equaliser against Fulham, could not match United for quality – a Rashford jink-and-shot from an angle illustrated this. For the second half Solskjær put on Edinson Cavani for Fred, the striker going to No 9, with Rashford wide left and Paul Pogba in midfield. It reaped a rich dividend as the players matched their manager’s positivity by tearing through Burnley to score. Rashford nutmegged Lowton, dashed down the left and pinged in a cross to Bruno Fernandes, who dummied for Greenwood to beat Bailey Peacock-Farrell. Yet delight for United soon turned to despair. Ashley Westwood curved a corner over from the left and first Aaron Wan-Bissaka lost James Tarkowski, then Harry Maguire could not hold off the Burnley centre-back, and Tarkowski’s header went in, to Henderson’s left. This added to the catalogue of strikes conceded from set pieces by Solskjær’s men, who had to shake themselves off and seek to breach Burnley again. In Rashford they had a man intent on doing this alone. One touch that had the ball squirming under his boot then releasing past the banked yellow-shirted defence had those inside the stadium gasping. Rashford’s control let him down, though, when Maguire fired a pass into him in front of Peacock-Farrell, the ball squeezing away. The keeper next made a sharp save low to his right from a Fernandes header but now came Greenwood’s intervention – scoring via a deflection off Jack Cork – and that of Cavani, who rounded off a quick break. While Burnley are six points clear of Fulham in the last relegation berth, United are giving City something to ponder, at least.