City started brightly at Villa Park, with the ball being worked into promising wide areas that lacked a more pinpoint delivery. The hosts did, however, grow into the game and saw Ollie Watkins' movement pose plenty of problems to City's high defensive line. The England international's uncharacteristic struggles in the final third continued as he failed to make the most of opportunities that came his way.
Cash endured no such issues when breaking the deadlock in the 19th minute. Bernardo Silva and Haaland failed to close the Villa full-back quickly enough on the edge of the box, allowing him to drift onto his left foot from 20 yards out and crash a left-footed effort into the bottom corner.
Haaland fired a tame effort at Emi Martinez as City sought an immediate equaliser, while Josko Gvardiol did Morgan Rogers a favour when making little of an apparent shove inside the penalty area, but Villa came closest to a second before the break as captain John McGinn fizzed another strike from distance narrowly past the post.
Haaland has 24 goals for club and country this season, with Tottenham the only team to have kept him out before running into Villa, but the prolific Norwegian was surprisingly quiet as City lacked an attacking spark as a collective.
They were unable to turn possession into something more tangible, with Villa prepared to sit deep and break out on the counter. Savinho almost forced a leveller on the hour mark, but his low drive from seven yards out was somehow flicked over the crossbar by Pau Torres. Former City academy star Jadon Sancho forced Gianluigi Donnarumma into a double save at the other end, before Haaland had a goal disallowed for offside and painfully collided with the post as Villa held on.