Nigel Clough was delighted to make a winning start as Sheffield United manager.
A dream start for the former Burton and Derby boss saw the Blades build on their win over Port Vale last weekend and the draw at Peterborough on Tuesday night.
Harry Maguire's first-half brace set the South Yorkshire side on their way. The 20-year-old defender twice headed home unmarked in the opening half an hour before Ryan Flynn sealed the three points early in the second half.
Alex substitute Max Clayton grabbed a late consolation goal as his side slipped into the Sky Bet League One relegation zone, below Clough's team on goal difference.
"We scored three goals for the first time this season and it's been a great week," said Clough, who was unveiled as David Weir's successor on Wednesday afternoon.
"Chris (Morgan, caretaker manager) has looked after them for the majority of the time and seven points out of nine gives us something to build on.
"We looked leggy in the last 15 minutes, that's understandable. I think when you've been losing games it takes an awful lot out of the players.
"The hardest part is to get the team on the pitch competing and that's what we aim to do in the next however long we've got.
"I think what we've seen is the honesty of the players in the first few days, they're very honest bunch. They work very hard, as they did today. There are little things we've got to work on, a little bit of quality here and there, but I think when you've got an honest group then it gives you a start."
Following the victory, Clough said it was difficult to predict where the Blades may finish at the end of the season.
He added: "I don't know, it's too early to tell. The main priority is to get away from trouble, get towards safety and see where we go from there."
Crewe manager Steve Davis was left to rue individual mistakes.
Aside from the goals, Davis felt there was little between the two sides.
"If we're looking at chances, looking at stats - which I don't particularly take much notice of, but I think they were important today - we probably had more efforts, more chances," said Davis.
"Again, we've conceded two ridiculous goals (Maguire's), which I think we did here last time.
"We've got done on two poor bits of marking. The game itself, I didn't think there was much in the game itself in terms of possession or anything like that.
``If you take the goals out of the first half, both teams probably would have been quite happy coming in nil-nil. So I'm disappointed from that aspect, obviously, because at nil-nil we would've really fancied ourselves second half.
"Byron (Moore) had a great chance after half-time to make it 2-1, that would've really stretched them. The confidence would have sapped from them very quickly if we could get that goal and put them under pressure. You could sense it with the crowd - even at 3-1.
``We had another couple of little chances, we hit the crossbar and they were getting a little bit nervy - we'd be the same in that situation because of where we're in the league."