George Blanda had the most games with 4+ passing touchdowns, with 340 games.

most games with 4 passing touchdowns career
Interpreted as:
most regular-season games by a player with 4 or more passing touchdowns career
BlandaBradyFavreBreesManningMorrallTarkentonRiversMarinoRoethlisbergerManningElwayTestaverdeHadlAllenTupaJurgensenKriegRyanDawsonUnitasHasselbeckMoon340308302287266255246244242239236234233224222220218213211211211209208
NAMEGPTDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
George BlandaGeorge Blanda3402361,9114,00747.726,9206.779.25.92776.9129460.6
Tom BradyTom Brady3086026,98110,90164.081,4797.5264.55.51941.85303,33397.6
Brett FavreBrett Favre3025086,30010,16962.071,8387.1237.95.03363.35253,48786.0
Drew BreesDrew Brees2875717,14210,55167.780,3587.6280.05.42432.34202,99198.7
Peyton ManningPeyton Manning2665396,1259,38065.371,9407.7270.55.72512.73031,95396.5
Earl MorrallEarl Morrall2551611,3792,68951.320,8097.781.66.01485.55848774.1
Fran TarkentonFran Tarkenton2463423,6866,46757.047,0037.3191.15.32664.12742,33780.4
Philip RiversPhilip Rivers2444215,2778,13464.963,4407.8260.05.22092.64652,84295.2
Dan MarinoDan Marino2424204,9678,35859.461,3617.3253.65.02523.02701,93086.4
Ben RoethlisbergerBen Roethlisberger2394035,2038,07364.461,8637.7258.85.02052.55283,49793.8
Eli ManningEli Manning2363664,8958,11960.357,0237.0241.64.52443.04112,87084.1
John ElwayJohn Elway2343004,1237,25056.951,4757.1220.04.12263.15163,78579.9
Vinny TestaverdeVinny Testaverde2332753,7876,70156.546,2336.9198.44.12674.04172,99275.0
John HadlJohn Hadl2242442,3634,68750.433,5037.1149.65.22685.71791,51467.4
Marcus AllenMarcus Allen2226122744.428210.41.322.213.7632106.8
Tom TupaTom Tupa2201225950451.43,4306.815.62.4255.04737260.5
Sonny JurgensenSonny Jurgensen2182552,4334,26257.132,2247.6147.86.01894.49474882.6
Dave KriegDave Krieg2132613,1055,31158.538,1477.2179.14.91993.74943,79481.5
Matt RyanMatt Ryan2113595,0337,68765.557,4357.5272.24.71622.14192,77694.6
Len DawsonLen Dawson2112392,1363,74157.128,7117.7136.16.41834.91671,42382.6
Johnny UnitasJohnny Unitas2112902,8305,18654.640,2397.8190.75.62534.97459078.2
Matt HasselbeckMatt Hasselbeck2092123,2225,33060.536,6386.9175.34.01532.93602,26082.4
Warren MoonWarren Moon2082913,9886,82358.449,3257.2237.14.32333.44583,41580.9
Craig MortonCraig Morton2071832,0533,78654.227,9087.4134.84.81874.93732,80073.5
Steve DeBergSteve DeBerg2061962,8745,02457.234,2416.8166.23.92044.12962,46974.2
StatMuse has season-level data for passing touchdowns going back to the 1921 season.