Interesting effect indeed!
Obvious thing first: don't use a pick when playing Knopfler parts! His tone is very much dominated by the particular way he plucks the strings with his fingers, often snapping them down on the fret board. Here, like often in his soloing, he's playing a double stop; he usually does this with the thumb and index finger, almost pinching together and dragging up the neighbouring strings and letting go of them. (Watch some videos of his solos; the right hand position looks really strange but works very well for this kind of stuff.)
This particular note has the characteristic attack largely shadowed because the tone is faded in à la steel guitar; note sure if he does this with the volume pot like Jeff Beck or with a volume pedal.
Now as for what he's actually playing at that particular spot... what I hear there is
X: 1
M: 4/4
K: Em
L: 1/4
V:C name="Guitar" clef=treble-8
z3 ([^d a] | [e g]
Which is essentially a ⅶ0 - ⅰ resolution, i.e. pretty classical dominant-tonic (except the bass and synth actually go to C instead of em, but that fits just as well to the E and G). The tricky bit is that the slurs are actually glissandi, i.e. bends – in counter-movement! Quite tricky, uncommon and certainly very effective. This can be done by playing the D♯ on the D string 13th fret with the ring finger and the A on the G-string 12th fret pre-bent (pulled, not pushed) one whole step with the middle finger, then releasing the G-string bend and simultaneously bending up the D♯ to E. It's just one movement.
Finally, again rather obvious, you need some overdrive to actually make it “growl”. Not a hard distortion, rather something tubescreamer-ish. Distortion on such a double stop creates intermodulation frequencies, i.e. basically tones that aren't really played on the guitar. Thus, as David Bowling comments, it's also possible that he actually just plays the simpler
X: 1
M: 4/4
K: Em
L: 1/4
V:C name="Guitar" clef=treble-8
z3 ([a c'] | [g c']
(which, at least when bent up rather than down, is quite a staple of bluesy solo playing), and the lower “counterpoint” voice is just imagined by my ears, being used to classical voice-leading.