The 41-year-old threw for 262 yards and engineered the game's only touchdown drive as Sony Michel punched the ball in to give New England the lead midway through the fourth quarter.
Julian Edelman – voted MVP with 141 yards receiving – and Rob Gronkowski also shined for New England, who now tie the Pittsburgh Steelers for the most Super Bowl championships.
The pair had 228 of New England's 262 receiving yards, with both nabbing key receptions in the touchdown drive.
With the Patriots needing a score to tighten their grip on the Vince Lombardi trophy, Brady delivered.
Starting at their own 31, the veteran quarterback found Gronkowski with a short pass for 19 yards, then, out of the gun, hit Edelman for a 13-yard completion.
Now at the Rams' 38-yard line, Brady found Rex Burkhead with a short seven-yard pass before finding 87 again as Gronkowski beat two defenders to finish two yards shy.
This was the only redzone visit of the night and Michel took advantage of good blocking to score his sixth postseason touchdown.
Plaudits should also go to the New England defence, who contained Jared Goff to just 229 yards and the Rams to just three points – having scored an average of 32.9 per game in the regular season.
The strong Patriots defensive performance was capped off when Stephon Gilmore read Goff and secured a pick on the New England two-yard line with just over four minutes remaining.
Super Bowl LIII was the lowest-scoring championship game in the history of the NFL, and it was the Rams who has their tails up early when cornerback Nickell Robey-Coleman tipped Brady's pass and linebacker Cory Littleton slid in for an interception.
However Los Angeles were unable to capitalise going three-and-out – bringing in punter Johnny Hekker for the first of his six punts in the opening 30 minutes.
The Rams failed to convert a third-down in the first half, and finished the opening half with 57 yards on offence.
But crucially, the New England offence was unable to put anything on the board in the first quarter – Stephen Gostkowski missing a 46-yard field goal.
Gostkowski was true with the boot from 42 yards early in the second as the Patriots went into the locker room 3-0 up.
The second half started in a similar vain to the first with defences prevailing and punters drafted in on three-and-outs.
Hekker grabbed himself a Super Bowl record when he sent the ball down 65 yards on a third-quarter punt – beating the old record by a solitary yard.
On their ensuing possession, the Rams drew the game level as Goff drove his side 42 yards including a deep pass to Robert Woods for 18 yards.
A vital sack on third and seven meant Los Angeles had to settle for three, with Greg Zuerlein doing the honours.
It would turn out to be the Rams' only score all night as the Patriots found the end zone for a 10-3 lead with seven minutes left before Goff was picked off with less than five remaining.
Gostkowski made it a two-score game late in the fourth when he converted a 41-yard attempt.
For the Rams, it was do or die.
A holding penalty brought the drive back before it had even begun, but as the 24-year-old pushed the Rams down the field, so the clock ticked down.
Zuerlein was drafted in for a 48-yard field goal attempt with eight ticks remaining, which would have reduced the deficit to seven.
The attempt veered left and Brady took a knee to secure the title.