Everton 0 Liverpool 2
However, this victory - their first since beating Manchester United over a month ago - was far from comprehensive.
But it moves Liverpool above Aston Villa into fifth place in the Premier League table, while Everton have won just once in 11 matches, leaving them just four points above the bottom three.
Benitez hasn't had much luck this season but there was certainly an element of fortune about Mascherano's 12th minute opener.
The early exchanges had been predictably frenetic with challenges flying in and neither goal threatened.
Mascherano unleashed a speculative shot from 30 yards which left Everton keeper Tim Howard flat-footed after taking a deflection of Joseph Yobo's outstretched leg.
The Argentina international will claim it but the defender's contribution was vital.
Within seconds, Everton spurned a chance to equalise as the atmosphere cranked up and an unmarked Diniyar Bilyaletdinov dragged his shot wide of the target with the goal at his mercy.
Liverpool's Pepe Reina was the busier of the keepers in the first half as Everton dominated both possession and territory.
He denied both Jo and Steven Pienaar but he could do nothing to stop Jo netting in 36th minute, although his effort was disallowed for offside.
Everton continued to dominate after the break with Reina stopping another fizzing Pienaar effort before making a telling double save.
First he sprawled to his left to deny Tim Cahill before then beating away Marouane Fellaini's fiercely struck follow-up.
In contrast, Liverpool looked nervous and lacklustre with Steven Gerrard enduring an uncharacteristically quiet Merseyside derby.
However, he played his part in Liverpool's decisive second goal 10 minutes from time
Yobo completed a miserable afternoon by shanking a defensive clearance and Gerrard pounced on the loose ball to set up substitute Albert Riera.
His powerful and angled shot was pushed clear by Howard but Kuyt was on hand to tuck away the rebound for his fifth of the season.