Elsewhere, Atletico Madrid and Espanyol kept alive their hopes of qualifying for the Champions League.
Left-footer Gomez began his career at Barcelona before switching to their city rivals Espanyol.
The win narrows the gap with leaders Real Madrid to seven points who host Espanyol on Sunday.
Club doctors and Italian paramedics tried to revive Jarque, a product of the Espanyol youth system, but without success.
And all have been brought in on the cheap by Martinez - or in Gomez's case borrowed from Espanyol.
Elsewhere, Barcelona welcomed coach Tito Vilanova back from cancer surgery with a comfortable 4-0 win over city rival Espanyol.
Jarque collapsed and died at the age of 26 in August 2009 following a training session with his Espanyol team.
Swansea's first game of their pre-season tour is at Palamos against La Liga giants Espanyol on 25 July (1900 BST).
In Spain, big-spending Malaga are now level on points with third-placed Valencia after a 2-1 win at Espanyol on Sunday.
Also missing from the list are the Espanyol player Mohammed Al Yaacoubi Moha and the FAR Rabat goalkeeper Tarik Al Jarmouni.
Sevilla moved up to eighth place with a 3-0 win over Espanyol that further dented the Barcelona-based side's faint hopes of European qualification.
Fourth-placed Real Sociedad also drew, 2-2 at Espanyol -- whose defender Javi Lopez conceded an own-goal for the equalizer with 14 minutes left.
Everton are believed to have met Espanyol's asking price for Riera but the player is understood to have favoured a move to Anfield.
Pablo Piatti scored the winner three minutes from time for Almeria while Malaga boosted their hopes of survival after a 2-1 win at Espanyol.
Relegation-threatened Sporting Gijon went down 2-0 at Getafe while Espanyol came back from two goals down to earn a 2-2 draw against Real Sociedad.
Espanyol's unwillingness to meet that price led to the collapse of the Hedman deal after the goalkeeper had agreed terms with the La Liga outfit.
They held a conference at the stadium on Saturday where they heard from fans of Hamburg and Espanyol, who have some influence in board decision-making.
Joan Laporta, president of European champions Barcelona -- Espanyol's city rivals -- said on their official Web site: ""We are very shocked by this tragic event.
Atletico and Espanyol lie eighth and ninth in the table respectively, a point behind seventh-placed Athletico Bilbao -- who slumped to a 2-1 defeat at Osasuna.
Granada suffered a 2-1 home defeat by Mallorca, Espanyol drew 0-0 with Valladolid and Real Sociedad shared a six-goal thriller with Real Betis as it ended 3-3.
Arena AufSchalke in Gelsenkirchen, Espanyol's Estadi Montjuic in Barcelona, the Arena Hamburg and the National Stadium in Bucharest are the other stadia being considered for that competition.
In Tuesday's other action, Osasuna consolidated sixth place with a 2-0 win over Espanyol that lifted the Pamplona-based club four points clear of their opponents and Atletico.
Real Sociedad moved up to eighth with a 2-1 win at Zaragoza, while Barcelona's city rivals Espanyol eased relegation worries with a 4-0 win at Athletic Bilbao.
Alves was dismissed for a second booking in the 62nd minute after body checking Jose Callejon, but Espanyol could not take advantage of having an extra man.
Having clinched a fourth title in five seasons when second-placed Real could only draw with Espanyol on Saturday, Barca went behind five minutes after halftime in the Spanish capital.
But defeats at Espanyol and now Atletico, who move up to fifth with the victory, have undermined their title charge and given defending champions Real a glimmer of hope.
In the other La Liga games played Saturday, Valledolid held fourth-placed Malaga to a 1-1 draw, while Real Vallecano move up to eighth after a 2-0 win against Espanyol.
The Espanyol tie will see Argentine star Lionel Messi take to the field for the first time this year, after a record-breaking 2012 which saw him score 91 goals.
Vilanova, who was present for last weekend's 4-0 win over city rival Espanyol, faces six weeks of chemotherapy and radiotherapy following the operation which took place on December 20.
Sunderland will now turn their attention to alternative targets, with Derby's Malcolm Christie and Espanyol frontman Raul Tamudo among the names to be linked with them in recent weeks.
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