Tigers went behind after just seven minutes as Gabby Agbonlahor gave Villa the lead and the relegated visitors were off the boil in the first half.
A very comfortable first half for Villa ended with a reminder of just how slim their lead was as Abel Hernandez flashed a shot wide from the edge of the area before goalkeeper Sam Johnstone had to save in quick succession from Campbell and then Grosicki as Hull went into the break with some encouragement.
Slutsky's team carried that momentum into the second half with a sustained period of pressure and they deservedly equalised after 62 minutes when Kamil Grosicki took on Taylor and stood up a cross to the far post where 20-year-old Jarrod Bowen scored with a low volley - his first goal for the club.
Andre Green should have put Villa back in front with 10 minutes remaining but got his header all wrong from two yards out and directed the ball back across goal.
Richard Sutcliffe's Talking Point: Defensive inexperience causes early season concern for Tigers
"Hull City’s defence. Taking on the bookies’ favourites with a back four three-quarters made up of debutants was always going to be a risk. And so it proved, at least in the first half as the Tigers defended like strangers for long periods - perhaps understandably considering Ola Aina, Michael Dawson, Michael Hector and Max Clark had not played together as a four in pre-season.
"Aina looked shaky defensively in those opening 45 minutes but decent on the ball going forward, while Clark - who played most of his games for Cambridge United on loan last season in central midfield - seemed unsure whether to close down Ahmed Elmohamady or not, meaning the former Tiger was given free licence to cross.
After the break, however, there was a big improvement with Clark much more aggressive and Hector standing tall with countless clearing headers. He looks a good signing from Chelsea on loan, while Aina and Dawson could also be pleased with their efforts in snuffing out an expensively assembled home attack."
Reaction: 'We need new players' - Slutsky
Reacting to the draw, Slutksy said: "I am very proud, we have a team. Of course, we need new players but we have a core and we have leaders."
"We were much better after the first 15 minutes. We were very bad before that because we had some new players.
"Jarrod (Bowen) was our best striker in pre-season so this was not a surprise he scored for us today."