Drew Brees has the most games with 4+ passing touchdowns, with 37 games.

player with most games with four or more passing touchdowns
Interpreted as:
player with most regular-season games with four or more passing touchdowns
BreesManningBradyRodgersFavreMarinoUnitasRoethlisbergerWilsonManningBlandaRyanStaffordFoutsJurgensenTarkentonMahomesLuckFitzpatrickMcNabbBledsoeRomoKelly3735333023211716151413121212121211111111111010
NAMEGPTDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Drew BreesDrew Brees371629991,35673.712,9709.6350.511.9141.037245138.6
Peyton ManningPeyton Manning351538921,27070.211,7289.2335.112.0292.324151129.2
Tom BradyTom Brady331418541,20670.811,1909.3339.111.7110.951293134.9
Aaron RodgersAaron Rodgers301277191,01470.99,2119.1307.012.560.652358136.1
Brett FavreBrett Favre239752380165.36,5558.2285.012.1172.138221121.3
Dan MarinoDan Marino219153783764.27,2688.7346.110.9232.721161116.5
Johnny UnitasJohnny Unitas176829647662.24,93110.4290.114.3204.2119.1
Ben RoethlisbergerBen Roethlisberger167242361069.35,2568.6328.511.871.127169130.3
Russell WilsonRussell Wilson156534148969.74,4089.0293.913.351.032197133.1
Eli ManningEli Manning145933149666.74,1148.3293.911.9153.018147119.2
George BlandaGeorge Blanda136024043155.74,1949.7322.613.9194.4110.2
Matt RyanMatt Ryan124930442970.94,0719.5339.311.451.225142133.9
Matthew StaffordMatthew Stafford125232951464.04,0908.0340.810.1122.318112112.6
Dan FoutsDan Fouts125228645662.74,1679.1347.311.4132.9118.6
Sonny JurgensenSonny Jurgensen125123841157.93,8229.3318.512.4194.6109.4
Fran TarkentonFran Tarkenton124920633761.13,1259.3260.414.5103.0118.9
Patrick MahomesPatrick Mahomes114929142169.13,9849.5362.211.671.71369131.0
Andrew LuckAndrew Luck114529045663.63,7888.3344.49.981.81393115.3
Ryan FitzpatrickRyan Fitzpatrick114627442264.93,7748.9343.110.9143.31782116.0
Donovan McNabbDonovan McNabb114625335870.73,61610.1328.712.830.825148139.2
Drew BledsoeDrew Bledsoe114425038664.83,3508.7304.511.441.018104125.9
Tony RomoTony Romo104220629968.93,23610.8323.614.051.716109137.2
Jim KellyJim Kelly104418528564.92,7959.8279.515.4144.915112116.2
John ElwayJohn Elway104120831266.72,8329.1283.213.192.9886123.0
Philip RiversPhilip Rivers93619330463.52,6308.7292.211.8113.61681115.4
StatMuse has game-level data for passing touchdowns going back to the 1950 season.

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