It was a disastrous start for Spurs as Villa went ahead in the opening minute as they cut through the visitors' defence as though they were not there.
They beat the press in the left-back position, Rogers danced past Lucas Bergvall and slipped in Ramsey, whose shot went straight through Antonin Kinsky's hands and into the back of the net.
The blunderous goalkeeper then set up another chance for Villa as a wayward pass led to a turnover of possession and Donyell Malen fizzed an effort just over.
It was one-way traffic as Spurs were completely overrun in midfield, with Youri Tielemans and Ramsey both missing the target with decent opportunities, while Kinsky did make amends with a stretching save to deny Leon Bailey.
Spurs could easily have been 3-0 down, but they then missed a golden chance to equalise in the 24th minute.
Dejan Kulusevski set Mikey Moore free down the right and he put his cross on a plate for Son Heung-min, but the South Korean was denied by a brilliant save by Emiliano Martinez, who flung himself across goal to make a block.
Villa had another swarming attack soon after as Bailey brought another good save out of Kinsky with Ramsey hitting the follow-up into the outside of the post.
The second half saw an immediate improvement from Spurs, who replaced 17-year-old Mikey Moore with Yves Bissouma, and there was a sustained spell of pressure.
But that made them vulnerable on the counter attack and it should have been 2-0 just before the hour.
John McGinn advanced into the space and played in Ramsey, but this time Kinsky made an important save.
There was no stopping Villa, though, and they did double their advantage in the 64th minute.
Another surge forward saw Bailey tee up Malan, whose ball across the face of goal was cleared straight into the path of Rogers to poke home from close range.
New signings Rashford and Marco Asensio were introduced immediately afterwards as Villa smelled blood.
Rogers drove wide after combining well with Asensio, while Ramsey fluffed another one-on-one opportunity as Kinsky blocked well.
Rashford, playing for the first time since December 12, was gunning for a debut goal and overran the ball when he closed in on goal.
Spurs made it a nervy final five minutes when deadline-day signing Tel opened his account by converting Kulusevski's cross, but they lost again.
