Rotherham were ahead within four minutes, with Dan Barlaser picking out Crooks perfectly from a free-kick and the midfielder powering in a header.

Nakhi Wells called Rotherham goalkeeper Viktor Johansson into an early stop at the other end, with the Swede equal to the powerfully-hit free-kick.

Ben Wiles snatched at a chance from Michael Ihiekwe's deflected cross as the hosts attempted to double their lead.

A swift move at the other end saw Tyreeq Bakinson fire off target after Callum O'Dowda's storming run.

City goalkeeper Daniel Bentley then had to be alert to push Smith's effort from the edge of the box behind.

Rotherham were in the ascendancy before the break and after a strong penalty shout for a foul on Matt Olosunde was dismissed, Crooks fired over a decent chance from the edge of the area.

They got their second after 41 minutes, however, with Olosunde holding his run to beat the offside trap and then picking out Smith, who poked in from close range.

The visiting side brought on striker Famara Diedhiou for ex-Miller loanee right-back Jack Hunt in the second half in a positive switch to try and get back into the game.

An uneventful start to the second period certainly suited Rotherham more and it was they who had the first opening after the restart with Jamie Lindsay curling an effort wide.

Diedhiou's first real involvement was to volley at goal and force Johansson to make a save with his legs.

Rotherham substitute Freddie Ladapo was having much more of an impact and he twice troubled the City defence in a matter of minutes, with the second occasion seeing his shot diverted behind for a corner.

A neat move down the right almost saw Rotherham net a third but Lindsay's cross was volleyed into the side netting by Ben Wiles.

Rotherham went even closer to rounding off a perfect afternoon with Barlaser smashing a 20-yard free-kick at goal which Bentley had to instinctively punch over the crossbar.

Wells had the best opportunity in the six minutes of added-on time but his glancing header did not trouble Johansson and the Millers could celebrate a clean sheet as well as three well-deserved points.