A side containing five new faces eased past their League One opponents thanks to goals from Marvin Emnes and debutant Emanuel Ledesma.
Grant Leadbitter was denied an early goal on his Boro debut by Trevor Carson but played a key role in the opener.
His quickly-taken free-kick gave Emnes space to rifle an unstoppable 25-yarder past Carson.
Both teams struggled to generate much momentum, although Andy Bishop saw a threatening shot deflected wide.
Middlesbrough eventually extended their lead an hour in, Ledesma slamming home from close range after Carson had spilled Nicky Bailey's effort.
But the hosts replied within three minutes, Mark Hughes heading emphatically home from Steve Schumacher's corner.
The visitors threatened to restore their two-goal cushion almost instantly but Adam Reach saw his shot rebound off the inside of the post.
Efe Sodje was sent off in injury time to compound Bury's woes.