The former Espanyol midfielder pounced on a loose ball 10 minutes from time in Tuesday's clash at Bloomfield Road to sink a spirited Leeds side that finished a man down after Darren O'Dea earned a second yellow card.
Wing duo Matt Phillips and Tom Ince had Blackpool on the front foot during the first-half, but Leeds were a threat from set plays and on the counter attack.
Robert Snodgrass and Luciano Becchio went close as Neil Warnock's side grew into the game after the interval, but Martinez sent the majority of a sell-out crowd home happy.
Middlesbrough's 0-0 draw with relegated Doncaster means Blackpool are four points ahead of the seventh-place side going into the final two games of the season.
Lomana LuaLua - who bagged a brace in a 5-0 victory over Leeds at Elland Road in November - came into the Blackpool line-up in place of the ill Stephen Dobbie, while left-back Bob Harris dropped to the bench to accommodate Stephen Crainey.
Leeds boss Neil Warnock went with the line-up that finished Saturday's 4-1 win over Peterborough, meaning Paul Robinson and Danny Webber started in place of full-back Charlie Taylor and injured winger Robbie Rogers.
Darren O'Dea headed over from Robinson's cross when unmarked after Blackpool failed to clear a Leeds corner, but the hosts made most of the early running.
In the 10th minute, Bloomfield Road burst into song and applause to commemorate the 10th anniversary of former manager Billy Ayre's death, and Phillips almost provided a fitting tribute by darting in from the left and clipping a shot into the side netting.
Ince then effortlessly spun Robinson on halfway before surging towards the area and planting a shot over, and then visiting goalkeeper Andy Lonergan rushed from his goal to thwart Gary Taylor-Fletcher.
Shortly before the half hour, Ince collected a return pass from LuaLua and bundled through a clutch of challenge on the edge of the Leeds area to draw a fine save from Lonergan.
The game flowed engagingly from end to end as half-time approached and after Phillips nodded beyond the bar from Taylor-Fletcher's header across goal, Leeds top scorer Ross McCormack had a penalty claim waved away after he appeared to get the better of Crainey.
In the 44th minute Lonergan saved from LuaLua's free-kick after a meaty challenge from O'Dea on Taylor-Fletcher earned the Leeds defender a booking.
A counter-attack was launched moments later and Webber cut in from the left to draw a sharp near-post stop from Matt Gilks.
Some controlled possession from Leeds at the start of the second period failed to yield any clear cut chances and Lonergan was back in action after the hour, palming a LuaLua effort behind following some clever footwork from Ince.
It was a relatively isolated moment of encouragement for the Seasiders, who were becoming increasingly ragged, and Snodgrass had Gilks at full-stretch from a 67th minute free kick before Becchio - on for the injured Billy Paynter - headed over from Adam Clayton's searching cross.
Blackpool substitute Nouha Dicko had Lonergan at full stretch in the 78th minute and he was soon involved in the winning goal.
The on-loan Wigan forward engineered space on the right to cross towards Ince and, when his team-mate failed to get the ball under control, Martinez was on hand to stab home.
Webber headed off target as Leeds sought an immediate response, but their quest for a point was compromised when O'Dea sent Dicko sprawling.