Victor Lindelof produced sensational defensive work as he kept Villa, especially Ollie Watkins and Douglas Luiz, at bay.
Manchester United have strengthened their bid to finish in the top four with a 1-0 win over Aston Villa at Old Trafford.
The win means United have opened up a nine-point lead over fifth-place Tottenham, and Villa remain sixth, level on points with Spurs.
Meanwhile, Emiliano Martinez, and to a large extent, Aston Villa, breathed a sigh of relief in the 15th minute when United came close to breaking the deadlock.
Three United players drove forward, and Fernandes got on the end of a long pass before he laid a first-time ball across the face of the goal, which Martinez looked set to collect, but the goalkeeper lost his footing, and the slow pace of the ball saved the day for him. The ball went behind before Anthony Martial could pounce on it.
Villa appealed for a 19th-minute penalty, but they were dismissed. Emiliano Buendia was released behind and played a clever ball across the face of the goal, which Ollie Watkins would have tapped in had he not lost his footing.
Watkins alleged he had been fouled by Diogo Dalot, but the referee ordered the play to go on, and Alex Moreno lashed a shot that was parried away by David De Gea.
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United were denied by the post in the 28th minute as Villa survived again. Jadon Sancho received a ball before he found Casemiro at the edge of the box, and the Brazilian took a shot towards the near side, but his effort cannoned off the bar.
The Red Devils finally got the opener in the 39th minute through Bruno Fernandes. Casemiro released Rashford behind Villa's defense before Martinez parried onto the pitch his first-time shot. The ball fell in the six-yard box where Fernandes was, and the Portuguese managed to get to the rebound and consequently found the Villa net.
Villa started the second half strong and almost equalized in the 46th minute. Lindelof made a crucial intervention as he whipped the ball away from Watkins, who was ready to head Ashley Young’s cross into the goal.
Fulham were so fluid in their attack, but Lindelof managed to keep them at bay. At the hour mark, Watkins released Aaron Ramsey, who skipped a challenge, and as he was about to release a shot, Lindelof diverted the ball for a corner.
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United came close to scoring the second in the 73rd minute. Rashford went down after a Callum Chambers challenge, but his call for a penalty was dismissed. The Red Devils recycled the ball back to Casemiro, and his left-foot shot towards the bottom corner went just inches wide.
Lindelof came to the rescue again as he managed to clear the ball off the line in the 81st minute. Villa pushed for an equalizer, and Watkins drove into the area, Marcel Sabtizer’s clearance hit Luke Shaw and fell on Luiz, who thought he had found the top corner before Lindelof headed off the line.