The Nigerian striker took advantage of some hesitant defending by Granada's Inigo Lopez to turn and fire low into the bottom corner on 12 minutes.
After a bright start to the second period, the ex-Newcastle forward doubled his tally thanks to more poor defending by the visitors, burrowing his way into the box to slip a shot underneath Tono.
Rios continued his own goalscoring run by notching his third goal in four days with a neat finish 17 minutes from time, before Youssef El-Arabi grabbed a consolation for the visitors with his third goal in as many games.
Los Granotes have now won seven straight home games and were well worthy of a victory over a Granada side lacking in invention at one end and resilience at the other.
Lopez seemed to take his eye off the ball for the opener as he stumbled in possession, allowing Martins to rob the ball before turning and shooting perfectly into the corner to leave Tono standing.
Jose Barkero's free-kick flew just over as a disappointing first-half drew to a close but Levante started the second in ominous form, and Barkero should have doubled the lead when he was played in by Martins four minutes after the break, instead smashing the ball over from close range.
Tono then got down well to stop Martins' powerful header moments later, but the Nigerian soon turned Lopez and Borja Gomez with ease before firing a shot that slipped past the keeper at his near post.
El-Arabi had a couple of chances to pull one back immediately for the visitors, his first effort blocked following a goalmouth scramble, before the Morocco international curled an effort from the right edge of the area wastefully over the bar.
Following his brace against Twente on Thursday, substitute Rios made sure of the home victory with a side-footed finish past Tono after a sweeping move involving Martins, Barkero and Michel that put him through on goal.
El-Arabi did eventually pull one back for Granada with a solid finish from the centre of the area after being teed up by Odion Ighalo, but it was too little, too late for the Andalusians.