The result leaves them three points clear of Blackburn Rovers and Millwall, who occupy seventh and eighth respectively.
If Sheffield United win their final two games - away to QPR and at home to Fulham - they will finish in the play-offs and could face Huddersfield Town in the semi-finals or the final at Wembley, with the Terriers having assured their place in the top six with victory over Barnsley last week.
The Blades need just four points to finish above Blackburn and Millwall, providing both clubs win their final two games.
Middlesbrough can reach a maximum of 73 points this season. They would need Sheffield United to draw at least one of their remaining games to catch them and then hope their goal difference is enough to help them finish above their Yorkshire rivals.
Boro's goal difference is four behind the Blades but with a game in hand, they do have the opportunity to claw that back.
Essentially, if Middlesbrough drop points, the Blades know four points will guarantee them top six while if Blackburn or Millwall stumble even fewer points will be needed to extend their campaign by at least two games.