Ole Gunnar Solskjaer's men have responded positively to disappointing 2-0 defeat to then bottom-of-the-table Watford less than a week ago to head into the new year with fresh belief they can secure a return to the Champions League next season.
Man United complacent against mid-table teams: Lingard
If United are to achieve that goal, Martial and Rashford will be key and they again provided the goals for the Red Devils in a game of few clear-cut chances.
There were also positives for Solskjaer at the back as his side 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.
Rashford was first to threaten when he hit the outside of the post midway through the first half.
Man United further behind in development than expected: Solskjaer
But Burnley were architects of their own downfall just before half-time when Charlie Taylor gifted possession to Andreas Perreira and he fed Martial to score his third goal in two games.
Phil Bardsley forced David De Gea into a fine save with Burnley's only shot on target.
United finally got the second goal their performance deserved to add a shine to the scoreline deep into stoppage time.
Daniel James led a counter-attack down the right and Rashford slotted home his 16th goal of the season at the second attempt after slipping as he rounded Nick Pope.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ