Tom Brady has the most career wins by a quarterback in the playoffs, with 34 wins.

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yes which quarterback has the most victories in nfl playoff history
BradyMontanaManningYoungElwayBradshawRoethlisbergerFavreStaubachRodgersMorrallAikmanFlaccoRutledgeWilsonBreesMcNabbWarnerReichKellyStarrManningBrunell3416141414141313131212111010999999988
NAMEGPWCMPATTPCTYDSAVGYDS/GTDTD%INTINT%SCKSCKYRATE
Tom BradyTom Brady45341,1061,76462.712,4497.1276.6834.7382.27244690.4
Joe MontanaJoe Montana231646073462.75,7727.9251.0456.1212.94627395.6
Peyton ManningPeyton Manning27146491,02763.27,3397.1271.8403.9252.44029887.4
Steve YoungSteve Young221429247162.03,3267.1151.2204.2132.82612885.8
John ElwayJohn Elway221435565154.54,9647.6225.6274.1213.23931879.7
Terry BradshawTerry Bradshaw191426145657.23,8338.4201.7306.6265.72418483.0
Ben RoethlisbergerBen Roethlisberger221346974463.05,7577.7261.7344.6283.85135186.4
Brett FavreBrett Favre241348179160.85,8557.4244.0445.6303.83623486.3
Roger StaubachRoger Staubach201322341054.42,7916.8139.6245.9194.66139076.0
Aaron RodgersAaron Rodgers211248174564.65,6697.6270.0456.0131.750338100.5
Earl MorrallEarl Morrall15125010348.58067.853.732.976.841456.5
Troy AikmanTroy Aikman161132050263.73,8497.7240.6234.6173.43421888.3
Joe FlaccoJoe Flacco151025344756.63,2237.2214.9255.6102.22818488.6
Jeff RutledgeJeff Rutledge141011100.02323.01.600.000.000118.8
Russell WilsonRussell Wilson16927545161.03,7868.4236.6255.5122.74927195.3
Drew BreesDrew Brees18948172166.75,3667.4298.1375.1152.12920697.1
Donovan McNabbDonovan McNabb16934157759.13,7526.5234.5244.2172.94830880.0
Kurt WarnerKurt Warner13930746266.53,9528.6304.0316.7143.019116102.8
Frank ReichFrank Reich1496710464.47837.555.976.732.984697.6
Jim KellyJim Kelly17932254559.13,8637.1227.2213.9285.12516872.3
Bart StarrBart Starr10913021361.01,7538.2175.3157.031.4104.8
Eli ManningEli Manning12824240060.52,8157.0234.6184.592.32715587.4
Mark BrunellMark Brunell14815630750.81,8336.0130.9113.6113.61910266.3
Dan MarinoDan Marino18838568756.04,5106.6250.6324.7243.52214177.1
Jim PlunkettJim Plunkett10816227259.62,2938.4229.3114.0124.42721281.9