The striker’s stunning effort on the hour gave the visitors a victory which they merited on the balance of play at the Mazuma Stadium.
In came Kelvin Mellor and Alfie McCalmont for Greg Leigh and Adam Phillips, while the absences of Kyle Letheren and Andre Da Silva Mendes meant no keeper on the Morecambe bench.
A Rotherham side looking for promotion back to the Championship was always going to prove a test of the Shrimps’ fine start to the season.
They certainly had the better of the opening stages as, with a strong wind behind them, they looked to either hit Smith and strike partner Joshua Kayode or turn the Morecambe backline and get them facing their own goal.
Smith saw an early shot deflected through to Jokull Andresson but that was as near as they came in the opening stages.
Having withstood that early pressure, the Shrimps established a foothold as playing into the wind suited their approach.
Arthur Gnahoua curled one effort wide after good work from Josh McPake before seeing another shot blocked by Shane Ferguson.
However, as the half progressed, the pendulum swung back Rotherham’s way with Andresson holding Ben Wiles’ shot before making two more routine saves from Smith.
There was still time before the break for Sam Lavelle to block another Smith effort as half-time arrived with honours even.
The second period opened as the first ended with the Millers again enjoying plenty of early possession inside the Morecambe half.
Wiles fired over inside the first half-minute before Andresson failed to hold a free-kick and the Shrimps somehow managed to clear the ball.
Stockton lashed a rare opportunity wide at the other end before the deadlock was broken on the hour.
Josh McPake lost possession, allowing Rotherham to break and Smith ran at the defence before curling a 25-yard effort over Andresson.
McCalmont shot wide at the other end as the Shrimps huffed and puffed in search of an equaliser despite the introductions of Phillips, Wes McDonald and Shayon Harrison.
McDonald fired one effort out of the ground and McCalmont saw another blocked but that was as near as they got.
Andresson tipped a late effort from Rotherham substitute Kieran Sadlier onto the top of the bar as, despite almost eight minutes of added time, the Shrimps were unable to get back on level terms.
Morecambe: Andresson, Cooney, O’Connor, Lavelle, Mellor, McLoughlin (Phillips 66), Diagouraga, McCalmont, Gnahoua (McDonald 68), Stockton, McPake (Harrison 76). Subs not used: Jones, Mensah, Pye, Wootton.
Rotherham United: Johansson, Harding, Ihiekwe, Edmonds-Green (Wood 46), Ogbene, Wiles, Lindsay, Rathbone, Ferguson (Mattock 72), Smith, Kayode (Sadlier 78). Subs not used: Chapman, Odoffin, Barlaser, Miller.
Referee: David Webb.