Sinfield scored a try and booted eight goals from 10 attempts to pass Lewis Jones’s tally of 2,920 points for Leeds.
The Rhinos fell behind to Vinnie Anderson’s try but rallied to lead 32-4 at half-time and Zak Hardaker also had plenty to celebrate with a hat-trick of tries.
Salford started promisingly with Daniel Holdsworth’s kick bouncing nicely for Anderson to mark his return with his first try of the season.
Leeds hit back with Chris Clarkson racing onto Sinfield’s well-timed pass for Hardaker to finish off smartly.
Sinfield’s conversion edged the Rhinos ahead but they missed the chance to increase the advantage when Brent Webb failed to take Brett Delaney’s pass.
Salford’s relief was only temporary with Webb sending Delaney over and Sinfield obliged with the conversion.
Danny McGuire’s 90-metre sprint was only stopped by a superb Luke Patten tackle but Leeds spun the ball out wide for Kallum Watkins to round Stuart Howarth with ease. Salford’s task became even tougher when Sinfield collected Ben Jones-Bishop’s kick for his first try of the season but he was off target with the conversion attempt.
Leeds added a sixth when Carl Ablett gathered McGuire’s kick for Liam Hood to notch his third try in three sub appearances.
The Rhinos made it 32-4 at the break with Sinfield and Watkins combining for McGuire to cross in the corner.
Salford, jeered off at the interval, lost concussed Chris Nero early in the second half.
Hardaker showed his star potential with a scorching solo run for his second try by waltzing through a pedestrian defence, with Sinfield’s conversion making it 38-4. Hardaker completed his hat-trick with Sinfield booting his record-setting goal.
Burrow scooted over for the Rhinos’ ninth before Ablett crossed in front of 6,891 fans - the Reds biggest crowd at their new stadium. Salford had to wait until four minutes from time before their second try from Gareth Owen, which was converted by Holdsworth. Patten gave the scoreline more respectability.
Salford Reds: Patten, Gibson, Nero, Gleeson, Williams, Holdsworth, Smith, McPherson, Howarth, Jewitt, Ashurst, Anderson, Wild. Substitutes: Adamson, Paleaaesina, Owen, James.
Leeds Rhinos: Webb, Jones-Bishop, Watkins, Hardaker, Hall, Sinfield, McGuire, Leuluai, Burrow, Peacock, Clarkson, Delaney, Ablett. Substitutes: Kirke, Griffin, Moore, Hood.
Referee: R Hicks (Oldham).