Kewell came into the contest without a win since taking over from Kevin Nolan at the start of the month and was given hope early on through Robert Milsom's driven effort.
But, as was previously the case against both Grimsby and Stevenage, Notts' suspect defence soon allowed Crewe an equaliser courtesy of Jordan Bowery.
That setback however proved temporary in the end as a dominant second half showing saw Kewell's men reap their rewards through Elliott Hewitt just past the hour-mark.
Speaking after the game, a relieved Kewell praised his players for their persistent performance.
"It’s a big relief," the 40-year-old said. "We’ve been working hard over the last couple of weeks and the performances have shown we are heading in the right direction.
"I feel the second half was the best 45 since I’ve been here. We changed a few things around at half-time and I felt we dominated.
"We were aggressive, we were picking up second balls and we were predominantly playing in their half.
"I am delighted for my staff, the players, the fans that we have got the three points."
The win moves Notts off the bottom of the league and leaves them just one point above the drop zone ahead of Wednesday's (AEST) clash with Kewell's former club Crawley Town.
Kenneth Dougall also tasted League Two success overnight, playing the full 90 minutes as Barnsley came from behind to defeat Fleetwood Town 3-1.
While Ryan McGowan and Cameron Burgess had to settle for 0-0 draws with Bradford City and Scunthorpe United respectively.
Australia's Championship contingent meanwhile had a tougher time of things with Socceroos duo James Meredith and Massimo Luongo both on the losing end for Millwall and Queens Park Rangers.
Luongo was unable to impact proceedings in a 3-0 loss to Swansea City and picked up a yellow card for his troubles.
Fellow Socceroos midfielder Jackson Irvine also received a booking during Hull City's 1-1 draw with promotion-favourites Middlesbrough and Ryan Williams created two goals to guide Rotherham United to a 2-2 draw with Stoke City.
Mat Ryan and Aaron Mooy were less successful in the Premier League, with both Brighton and Huddersfield losing out comfortably to Manchester City (2-0) and Tottenham Hotspur (2-0) respectively.
Goalkeeper Danny Vukovic continued his hot start to the Belgian First Division A with a clean sheet in Genk's 4-0 victory over Zulte Waregem.
Awer Mabil produced an assist in Midtjylland's 5-2 Danish Superliga thumping of Hobro and Aleksandar Jovanovic earned a clean sheet in the centre of defence as Jeju United edged K League 1 rivals Jeonnam Dragons 1-0.
In Scotland, Tom Rogic came off the bench to help Celtic see off Aberdeen, as did Oliver Bozanic for Hearts in the Premiership leaders' 2-1 win over St Johnstone.
And Ryan Edwards' St Mirren went head to head with Mark Milligan's Hibernian in a match that saw Hibs snag a 1-0 victory and maintain their one point lead above the Hoops and Kilmarnock in second place.
