Boasting fresh legs after last week's bye, the Blues held off a relentless Giants side 12.16 (88) to 9.11 (65) at Engie Stadium on Saturday to make it five wins from five games under Fraser.
After losing eight of nine games under former coach Michael Voss, the Blues are 12th (six wins, eight losses), sitting outside the top 10 on percentage.
Sam Walsh (one goal, 34 disposals, five clearances) was again influential at the contest, well supported by Patrick Cripps (33 disposals, seven clearances) and George Hewett (one goal, 30 disposals, five clearances).
Francis Evans kicked three goals, while former GWS player Wade Derksen (eight intercepts) impressed in a defensive unit missing the injured Jacob Weitering.
The 11th-placed Giants (6-8) lament another missed opportunity to cement their finals spot, suffering back-to-back defeats after last week's loss to 10th-placed St Kilda.
Finn Callaghan led the home side with 31 touches and seven clearances, while fired-up skipper Toby Greene (three goals) tried to spark his side.
Despite Weitering's absence, Giants spearhead Jesse Hogan was again limited to one goal in his second game on return from a hip injury.
The Giants were better with their chances in a tight opening quarter to take a five-point lead into the first break.
But Carlton upped the pressure and leaped ahead thanks to back-to-back goals from Evans.
GWS swingman Conor Stone matched Evans' feat to momentarily reduce the deficit to two points, before a goal from Will Hayward helped keep the Giants at arm's length at halftime.
Greene sparked a chain of four GWS goals to bring the score level at 9.7 (61) to Carlton's 8.13 (61), but Walsh kicked an after-the-siren major to restore the visitors' lead to six points.
Carlton finally broke away when Hayward kicked off the final quarter with a booming kick from outside the 50-metre arc for his second goal.
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