And delighted Crewe boss Dario Gradi admitted: "The win means we have made a good start to the season.
"If we had lost today then you would have said we've had a poor start to the season but the win means we've had a good start but - that's how fine it is.
"We came to Rotherham and knew we would have to weather the storm. We did that in the first half and got the added bonus of the penalty.
"We played a lot better in the second half and coped with them a lot better. Goals are still hard to come by and we had to rely on set pieces but it was nice to pick up the win.
Ashton gave Crewe a first-half lead seconds before the break with his third goal of the season.
The 19-year-old striker, who is being tracked by a string of Premiership clubs, showed his class three minutes before the break when his free kick cannoned off the Rotherham wall.
He pounced on the ball, whipped in the cross and Guy Branston held down Steve Jones in the area. Ashton took the penalty and coolly smashed it past Mike Pollitt in front of Crewe's travelling fans.
Three minutes into the second half Ashton again caused Rotherham nightmares at the back when he squeezed through a gap but drilled his low shot wide.
Rotherham's new recruit Martin Butler - a £150,000 capture from Reading - made a promising debut and went close with a clever overhead kick six minutes into the second half but Clayton Ince collected.
And four minutes later Butler stabbed another shot towards goal but the keeper was well positioned.
Seconds later Crewe stretched their advantage when another Kenny Lunt free kick fell for Walker who forced the ball over the line as Pollitt scrambled to reach it.
And when Steve Jones broke away he should had added a third but Pollitt snatched it away.