Leighton Baines cleared a Ben Gibson header off the line from a corner as Boro dominated in the second half and Everton keeper Joel Robles made a brilliant save late on, palming a fierce header from Rudy Gestede over the bar.
The result means Everton stay seventh in the table, while Boro, who travel to fellow strugglers Crystal Palace next, are still in 15th place, two points above the relegation zone.
(Reporting by Simon Jennings in Bengaluru, editing by Pritha Sarkar)
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