But after spending much of the game camped in their own half by Millwall's enterprising play, Crewe manager Dario Gradi was quick to pay tribute to his side's true grit.
Millwall may have endured a miserable time since relegation along with their hosts from the Championship, but they were in the ascendancy for long spells.
And had it not been for an outstanding save from Ben Williams when he kept out Alan Dunne's first-half header they might have gone on to get something from the game.
But while the Lions have only won once, Crewe's victory was their fourth of the campaign and their second in a week and they are now up to seventh in the table.
After labouring for an hour, Gradi's tactical switch paid dividends with Welsh international David Vaughan moved forward from midfield breezing past a couple of challenges to set up Varney on the right of the box.
And the striker, who opened his account for the season against Cheltenham last week, coolly finished with a rising shot past Chris Day in the 65th minute.
Had the speedy Jon Otsemobor matched his running with a clinical finish when substitute Rodney Jack put him through on goal in the closing stages, Crewe would have avoided the need to negotiate a nervy finish.
Millwall substitute Zoumana Bakayogo had the goal at his mercy but volleyed over leaving the Lions to rue not converting some of their earlier dominance into goals.
After Williams had palmed away Dunne's close-range header, Crewe should have scored when Otsemobor's surging run released Gary Roberts in on goal, but with just Day to beat he pulled his shot wide of the post.
Williams saved again from danger man Poul Hubertz at the close of the first half. The same player came close with a 25-yard drive after cutting in from the left.
Crewe lacked fluency for most of the afternoon, but when Maurice Ross slipped 10 minutes into the second half, Varney was through on goal only to drag his effort wide of the far post.
But he made amends shortly after finishing off Vaughan's approach play with confidence.