Bamford, who is on loan from Chelsea, opened the scoring with a precise shot in the eighth minute and Wildschut showed real class and composure to double the lead 11 minutes later before Tomlin rounded off the scoring with three minutes left.
Rotherham’s predicament worsened when top scorer Alex Revell was substituted after being caught by a high wayward Boro boot.
However, his replacement Jordan Bowery lasted little more than four minutes before he was given a straight red card for aiming a low kick at George Friend.
There was no way back for Steve Evans’ side and although they tried to make an impression in the second half, Boro thoroughly deserved the victory.
Rotherham started the match unbeaten in five in 16th and looking for their first win against Boro since New Year’s Day 1966 while the visitors were looking to return to winning form after one point from two games.
Rotherham attacked straight from kick-off and Jonson Clarke-Harris headed wide with less than a minute on the clock.
The pace in the opening stages was relentless although there was little composure before Boro went ahead in the eighth minute, albeit with a hint of a foul in the build-up.
Rotherham failed to clear and Bamford hurdled a defender who had gone to ground, collected the ball on the edge of the area, turned and released a crisp shot which gave goalkeeper Adam Collin no chance.
The visitors were more assured on the ball and they doubled their lead 11 minutes later after some neat interplay which ended with Wildschut jinking inside his marker and placing a left-footed shot into the top corner.
Rotherham’s attacking options took a blow a minute later when striker Revell was substituted after a lengthy delay to be replaced by Bowery.
However, he lasted just four minutes and 18 seconds. Penalised for a foul, his low kick at Friend resulted in a straight red.
Boro, though, were revelling in it and they should have got a third when Wildschut found Kike unmarked in front of goal but the Spaniard fired over.
The same player again fired high after Wildschut ran the length of the field before finding his colleague on the right of the area with Boro in complete control.
Rotherham managed to make it to the break without conceding another goal and started the second half brightly.
Lee Frecklington’s fierce shot forced Dimitrios Konstantopoulos to parry before Paul Green sent a ball across goal but wide of the post.
Boro responded with Kike’s half-volley pushed away by Collin and moments later the Spaniard was given plenty and time of space to fashion an opening only to produce a shot the keeper had no trouble getting down to smother.
Wildschut sent a low ball across the front of goal which the onrushing Bamford just failed to connect with despite a desperate lunge while Jelle Vossen sent a snap shot inches wide.
Rotherham should have pulled one back but Matt Derbyshire hit the post with the goalkeeper already diving the other way.
Instead, it was Boro who had the final say with Tomlin jinking through the box before sending a low shot to the right of the keeper and into the left-hand corner.