Santana's approach is pretty interesting because he uses relatively low gain amps (Mesa Mark I, Dumble, etc), dials them in really warm with heavily boosted mids and chopped treble, cranks them up, and then uses primarily his *bridge* humbucker while riding the *volume* knob to vary the response to his liking. Not sure if he keeps his tone knob slightly rolled off at all times or not, but you pretty much never see him touch it. He also doesn't really use pedals other than an occasional wah. The rest is in his fingers.
For the really smooth and tubular sound in the first video, Mark Barrios does pretty much the same thing, but he uses the neck pickup more and he had a newer Mark V around the time that clip was recorded based on what I could dig up. He does a lot of Santana covers live, so it's logical that you connected the two!
So, for what you want: A low gain amp dialed warm and running somewhat hot, a bit o' reverb, and manipulate the volume knob. Whether you use the bridge or neck pickup will depend a bit on your pickups and playing style. If needed, you can roll back the tone slightly and/or boost the mids with a tube screamer.
