Scholes, who was irrepressible in United's engine room all afternoon, struck five minutes before half time when he latched onto Teddy Sheringham’s elegant cross-field pass to rifle home his eighth of the season.
Solskjaer then stepped off the bench to provide his party piece and register the knockout blow by slotting home under the exposed Neil Sullivan to score his 50th league goal for United.
Spurs can take heart from a performance of genuine spirit and creditable bravery. However it takes more than that to win at Old Trafford these days.
United have not lost a league game at home for nearly two years. Ferguson's side had also scored in each of their previous 44 Premiership games at Old Trafford.
We had won just one of the previous 22 visits to Manchester United and George Graham made just one change with Chris Armstrong, who remains the last British player to score against United in the league, replacing the injured Sergei Rebrov.
Fabien Barthez added to the entertainment of the game but, in doing so, also caused a moment's panic when he dropped Chris Perry's looping header from Darren Anderton's free-kick, but United managed to scramble the ball clear.
United were attacking with pace and cohesion, the electricity of their movement equalling the speed with which they have opened up an eight-point gap at the top of the league. However Spurs, and in particular Chris Perry and Sol Campbell, were up for the fight.
Beckham delivered his trademark barrage of whipped crosses from the right and Scholes was dictatorial in midfield. But the Spurs back-line manfully repelled everything that was being thrown at them and counter-attacked buoyantly,
Having the best chance of the first half when Michael Silvestre provided Les Ferdinand with a free shot from the edge of the area. However the rejuvenated striker, with four goals from his previous two games, choked his effort and Barthez palmed the ball wide.
Butt tried his luck from long range and Roy Keane clipped inches wide after Beckham played him through but in the 40th minute Scholes made absolutely no mistake when presented with a clear sight of goal.
Sheringham spread the play beautifully from right to left where Scholes killed the ball in an instant before cutting inside Stephen Carr. Then after looking up to view the goal, he belted the ball past Sullivan for his eighth of the season and the opening goal of the game.
United have never lost a Premiership match at Old Trafford in which they have scored the first goal and, from that moment in, they never looked likely to lose that record.
As the game entered its final stages, United displayed their wealth of talent when they brought on the fit again Giggs and Solskjaer.
At 1-0, Spurs still had hope of snatching a point, and those dreams almost became reality when Ferdinand pulled the ball back past Barthez only for United to scramble it clear for a corner.
But United killed off those lingering hopes in the 84th minute when Solskjaer latched on to a back pass to slide the ball past Sullivan for United's second and his fifth of the campaign.
Man Utd: Barthez, G. Neville, P. Neville, Brown, Silvestre, Beckham, Butt (Giggs 72), Keane, Scholes, Yorke (Solskjaer 72), Sheringham.
Subs Not Used: Van Der Gouw, Irwin, Greening. Booked: Yorke, G. Neville.
Goals: Scholes 40, Solskjaer 84.
Tottenham: Sullivan, Campbell, Carr, Perry, Anderton, Sherwood, Ferdinand, Armstrong (Korsten 63), Clemence, King, Thelwell.
Subs Not Used: Walker, Freund, Davies, Vega. Booked: Ferdinand.
Ref: G Poll (Tring)
Despite the best efforts of a spirited Spurs, United relentless march towards another Premiership title continues. Fine finishes in each half from Paul Scholes and substitute Ole Gunnar Solskjaer wrapped up another victory for the champions.