Suarez has been involved in 13 goals in 13 La Liga appearances against Real Sociedad (seven goals and six assists)
Real Sociedad went back to the top of La Liga, although Luis Suarez's two goals for defending champions Atletico Madrid denied them victory.
La Real, who last won the title in 1982, led 2-0 when Alexander Isak set up Alexander Sorloth for the opener and then curled in a free-kick.
But Suarez pulled one back with a header from Joao Felix's cross.
And the veteran levelled with a penalty to make it 2-2 after he had been fouled by Mikel Merino.
Real Sociedad are one point above Real Madrid, who had gone top with a 2-1 win at Barcelona earlier in the day.
Third-placed Sevilla beat Levante 5-3 in Sunday's early game and Atletico are fourth - three points behind the leaders.
- Line-upsMatch StatsLive Text
Line-upsAtl Madrid
Formation 4-3-3
13Oblak23Trippier18Felipe22Hermoso12Lodi dos Santos5de Paul6Koke11Lemar8Griezmann9Suárez7Sequeira
- 13Oblak23Trippier18FelipeBooked at 31mins22HermosoSubstituted forHerreraat 73'minutes12Lodi dos SantosSubstituted forCorreaat 58'minutes5de PaulSubstituted forKondogbiaat 58'minutes6Koke11LemarSubstituted forCarrascoat 45'minutes8GriezmannSubstituted forSantos Carneiro Da Cunhaat 73'minutes9Suárez7Sequeira
Substitutes
- 1Lecomte2Giménez4Kondogbia10Correa16Herrera19Santos Carneiro Da Cunha21Carrasco24Vrsaljko
Real Sociedad
Formation 3-4-1-2
1Remiro Gargallo6Elustondo24Le Normand5Zubeldia2Zaldua16Guevara8Merino18Gorosabel21Silva19Isak23Sørloth
- 1Remiro Gargallo6ElustondoBooked at 68mins24Le Normand5Zubeldia2ZalduaBooked at 41minsSubstituted forTurrientesat 64'minutes16GuevaraSubstituted forJanuzajat 88'minutes8MerinoBooked at 76mins18Gorosabel21SilvaSubstituted forPachecoat 63'minutes19IsakSubstituted forPortugués Manzaneraat 64'minutes23SørlothSubstituted forLobeteat 89'minutes
Substitutes
- 7Portugués Manzanera11Januzaj13Ryan26Pacheco27Turrientes29Navarro35Lobete41Valera
Referee:José Luis Munuera MonteroAttendance:50,032Match StatsHome TeamAtl MadridAway TeamReal SociedadPossessionHome56%Away44%ShotsHome17Away8Shots on TargetHome4Away4CornersHome4Away3FoulsHome14Away14Live TextPost update
Match ends, Atletico Madrid 2, Real Sociedad 2.
90'+6'Full Time
Second Half ends, Atletico Madrid 2, Real Sociedad 2.
90'+5'Post update
Foul by Luis Suárez (Atletico Madrid).
90'+5'Post update
Robin Le Normand (Real Sociedad) wins a free kick in the defensive half.
90'+4'Post update
Foul by Felipe (Atletico Madrid).
90'+4'Post update
Julen Lobete (Real Sociedad) wins a free kick in the attacking half.
90'+3'Post update
Attempt missed. Geoffrey Kondogbia (Atletico Madrid) header from the centre of the box misses to the left. Assisted by Kieran Trippier with a cross following a corner.
90'+3'Post update
Corner, Atletico Madrid. Conceded by Mikel Merino.
90'+2'Post update
João Félix (Atletico Madrid) wins a free kick in the attacking half.
90'+2'Post update
Foul by Portu (Real Sociedad).
90'+1'Post update
Foul by Kieran Trippier (Atletico Madrid).
90'+1'Post update
Adnan Januzaj (Real Sociedad) wins a free kick in the defensive half.
90'+1'Post update
Attempt blocked. João Félix (Atletico Madrid) left footed shot from outside the box is blocked. Assisted by Ángel Correa.
89'Post update
Koke (Atletico Madrid) wins a free kick in the defensive half.
89'Post update
Foul by Julen Lobete (Real Sociedad).
89'Substitution
Substitution, Real Sociedad. Julen Lobete replaces Alexander Sørloth.
88'Substitution
Substitution, Real Sociedad. Adnan Januzaj replaces Ander Guevara.
86'Post update
Foul by Ángel Correa (Atletico Madrid).
86'Post update
Robin Le Normand (Real Sociedad) wins a free kick in the defensive half.
84'Post update
Felipe (Atletico Madrid) wins a free kick in the defensive half.
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Source: bbc.com