The visitors almost got off to a flying start, Anthony Forde struck a free-kick at goal which Rob Green did really well to save, from the re-bound of that save former Leeds United midfielder Tom Adeyemi was only denied by the post.
Pablo Hernandez had United’s best chance of the half in the 18th minute, he did really well to cut inside, before firing from the edge of the box, but his effort went just wide.
Danny Ward went close for Rotherham just after the half-an-hour mark, his deflected effort forced Green into another good save.
Darnell Fisher then did really well on the right flank to tee up Izzy Brown, but he could only fire over from 12 yards out.
Rotherham then had a good chance from a set-piece, after being re-ordered to take the intial corner, Anthony Forde’s cross
Souleymane Doukara tried a drive from range in added time of the first half, but he blazed his effort over the crossbar.
Half Time: Leeds United 0-0 Rotherham United
United came out of the blocks well in the second period and were soon in front when Kyle Bartley’s bullet header found the top left corner, from a Pablo Hernandez corner.
Leeds almost went further ahead soon after, Hernandez sent Roofe down the right flank and he put a fine ball across the box and Chris Wood was just inches away from poking it home.
Wood did make a breakthrough in the 66th minute, Liam Bridcutt put a cross in and the front-man chested down before superbly volleying the ball into the back of the net, to double United’s lead.
Gaetano Berardi almost added a third, he was played through on goal, he beat Lewis Price, but not the left post.
A minute later United did go three goals ahead, Roofe put in a fine low ball from the right flank, before Wood tapped home his second of the match.
Danny Ward came closest for Rotherham in the second period, his effort from a narrow angle could only find the side netting.
In the final minute of normal time, Dallas was felled, giving Hernandez the opportunity to strike on goal at a free-kick and he saw his effort cannon off the post, as Leeds recorded a fourth straight win and clean sheet at Elland Road.
Full Time: Leeds United 3-0 Rotherham United
Leeds: Green, Ayling, Bartley, Jansson, Berardi, Sacko (Vieira 45), Hernandez, Bridcutt, Roofe, Doukara (Dallas 73), Wood (Antonsson 82). Subs not used: Silvestri, Cooper, Phillips, Denton.
Rotherham: Price, Mattock, Broadfoot (Wood 84), Forde (Taylor 70), Frecklington, Ward, Fisher, Newell (Vaulks 76), Adeyemi, Belaid, Brown. Subs not used: Odemwingie, Halford, Blackstock, Bilboe.
Booked: Jansson (Leeds), Mattock (Rotherham).
Referee: S. Martin
Venue: Elland Road