Martins gave the hosts a flying start when his free-kick out on the left went through a gaping hole in the Sporting wall and beat Juan Pablo at his near post.
Sporting could not contain the hosts' passing and movement early on and Siqueira made it two as he received an excellent through-ball from Dani Benitez and coolly slotted past Pablo from close range.
Granada continued to have the better of the play after half-time as Benitez struck the bar and Ikechukwu Uche had a goal wrongly disallowed for offside before Adrian Colunga pulled a goal back for the visitors with a fine lob deep into stoppage time.
Abel Resino's side had come into the game only four points ahead of Sporting in the final relegation place after three consecutive defeats, but they responded in style with an attacking aggression that Sporting could not live with.
Martins did though get a bit lucky with the opener as his free-kick on three minutes should have been comfortable blocked by the wall which instead parted and allowed the ball to slip between Pablo and his near post.
The Portuguese midfielder then nearly doubled his and his side's tally from another free-kick that was deflected just over the bar.
Colunga curled Sporting's first real effort of the day just wide on nine minutes, but it was the hosts who continued to look the most likely to score again and they duly did so on 23 minutes.
Benitez and Siqueira pulled the Sporting defence apart with an exchange of passes down the left and the Brazilian remained calm to slot home his third goal of the season.
Benitez was putting in the type of performance that many had expected him to produce on a more regular basis this season and he nearly capped a fine individual display with a goal as he sent another free-kick in a dangerous area crashing off the bar.
Minutes later Uche was also denied a third as he turned in Mikel Rico's unselfish pass only to be flagged offside.
Oscar Trejo then missed Sporting's best chance to get back into the match as he took Nacho Cases' lovely through-ball in his stride but his finish was weak and Julio Cesar was able to make an easy save.
Franco Jara headed over another decent opportunity for Granada to extend their lead with four minutes remaining and Colunga gave Sporting the slightest glimmer of hope as he wonderfully lobbed Cesar from the edge of the area three minutes into stoppage time.
However, with barely enough time for the visitors to even launch another attack, the only drama left was a red card shown to Martins who had already been substituted for arguing with the assistant referee.