Cam Newton has the most games with 1+ passing touchdown and 1+ rushing touchdown, with 42 games.

players with most games with at least one passing touchdown and at least one rushing touchdown
Interpreted as:
players with most regular-season games with at least one passing touchdown and at least one rushing touchdown
NewtonYoungRodgersTarkentonKempVickCulpepperElwayGroganGabrielBreesMcNabbBradshawStewartBradyMoonDaltonGarciaMcNairCunninghamAllenPrescottWilson4231272423222222222221212120191918171717161616
NAMEGPPASS TDRUSH TDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Cam NewtonCam Newton4269518081,30362.010,3067.9245.45.3352.77046493.2
Steve YoungSteve Young31543659492464.37,5778.2244.45.8232.57539098.9
Aaron RodgersAaron Rodgers27542963495266.67,8658.3291.35.7161.762424103.9
Fran TarkentonFran Tarkenton24462536861060.35,2978.7220.77.5172.8102.1
Jack KempJack Kemp23392932864950.55,6058.6243.76.0355.477.7
Michael VickMichael Vick22382535860858.95,1958.5236.16.3162.65331396.6
Daunte CulpepperDaunte Culpepper22382645171663.05,6037.8254.75.3253.56433690.3
John ElwayJohn Elway22372438466757.65,2917.9240.55.5274.04836484.7
Steve GroganSteve Grogan22372528456850.04,1827.4190.16.5366.369.7
Roman GabrielRoman Gabriel22362431960652.64,5807.6208.25.9193.184.2
Drew BreesDrew Brees21472357281570.26,4507.9307.15.8162.038246104.6
Donovan McNabbDonovan McNabb21362241767162.14,8537.2231.15.481.24730696.9
Terry BradshawTerry Bradshaw21282424045752.53,0846.7146.96.1245.372.5
Kordell StewartKordell Stewart20332534257459.64,5047.8225.25.7173.04127191.3
Tom BradyTom Brady19422150375466.76,0328.0317.55.6101.339227104.1
Warren MoonWarren Moon19302036862059.44,6107.4242.64.8182.93021686.6
Andy DaltonAndy Dalton18281837360661.64,5397.5252.24.6233.83318484.2
Jeff GarciaJeff Garcia17321937357764.64,1757.2245.65.5101.72211397.4
Steve McNairSteve McNair17262029045863.33,6798.0216.45.771.530177100.9
Randall CunninghamRandall Cunningham17271726447455.73,6857.8216.85.7153.26040686.7
Josh AllenJosh Allen16281932147767.33,9198.2244.95.961.334230106.7
Dak PrescottDak Prescott16261832948368.13,9858.3249.15.440.828185107.7
Russell WilsonRussell Wilson16301934250767.54,4418.8277.65.981.641269107.9
Ben RoethlisbergerBen Roethlisberger16251633353562.24,0707.6254.44.7112.12519792.7
Peyton ManningPeyton Manning16291634854364.14,1867.7261.65.3152.82317893.9
StatMuse has game-level data for rushing touchdowns going back to the 1960 season.

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