Having snatched pole from his Mercedes team-mate, the 2008 world champion led from the front on Sunday as Rosberg was struck by technical problems.
They began as early as the parade lap when the German sat stationary on the grid, forcing him to relinquish second place and start from the pit lane.
He battled hard in the opening laps but was forced to retire on lap 14 as controls on his steering wheel failed, leaving him unable to change settings and handing the initiative to Hamilton.
The Briton took full advantage and, even though a mid-race safety car brought the pack back together, he claimed victory from the Red Bull pair of Sebastian Vettel and Ricciardo by over 13 seconds.
Fernando Alonso finished just off the podium in fourth, with Williams' Felipe Massa completing the top five.
Hamilton's win sees him move three points clear of Rosberg in the championship with five races - including Abu Dhabi's double-points season closer - remaining.
With no Rosberg at the start, Alonso and Vettel were able to make very quick starts and immediately jump Ricciardo to begin the chase to Hamilton.
The Mercedes driver did not look flustered, though, and began to open up a healthy lead by the first pit stops.
Hamilton, Alonso and Vettel had no problems but it signalled the end for Rosberg as his steering wheel failed to find any gear in his Mercedes.
Just after the midway stage the race saw a twist as the safety car was deployed as Sergio Perez (Force India) lost his front wing following a tangle with Adrian Sutil (Sauber).
With the cars bunching up behind the leader, Alonso took a chance by making an early pit stop and although it initially saw him drop down a place, the Spaniard finished strongly.
After the safety car returned to the pits, Hamilton burst clear of his rivals but his tyres were wearing and the Brit needed to work a gap in order to ensure he would see the chequered flag first.
Slowly he built a 22-second advantage before diving into the pits. Vettel assumed the lead briefly but the Mercedes was all over the back of the Red Bull and swiftly retook the lead the following lap.
The safety car introduction meant the race was unable to go the full distance of 61 laps in the two hour time limit, but it mattered little to Hamilton as he charged to a seventh race win of the season.