The much-hyped derby encounter, described as the biggest match in the history of the Premier League, was not the spectacle that many had hoped for but the local rivals still produced an absorbing encounter that a more adventurous City deservedly edged when Kompany was left free to head home from a David Silva corner.
United needed only a draw to retain top spot and, with fixtures against Swansea and Sunderland to come, almost certainly secure a 20th Premier League title. However, Sir Alex Ferguson's decision to deploy an unadventurous five-man midfield backfired as an emasculated United created little of note at a stadium where City have now won 17 of 18 league games this season.
As Ferguson became involved in a touchline row with Roberto Mancini on a deeply frustrating evening for the title-holders, the pretenders to the throne continued to exert control and following a nervous conclusion held on for a victory that puts them within touching distance of a first league title since 1968.
Wins in City's final two games - away at Newcastle and home to QPR - will now give Mancini's side the title, usurp United at the top of English football and signal a definitive shift in the balance of power in a city that has been characterised by red dominance for decades.
After a limp performance, and a remarkable failure to have even one shot on target in 90 minutes, United may reflect that a timid team selection proved their undoing on a night when they surrendered top spot, and possibly city supremacy, with a whimper.
While City were unchanged from the side that defeated Wolves 2-0, with former United striker Carlos Tevez a leading member of a what was expected to be a fluid and fluent front four, United adopted an unmistakeably conservative approach for a match they only needed to draw, Ferguson sacrificing Danny Welbeck in attack in order to bolster the midfield with Park Ji-sung. Antonio Valencia was also surprisingly replaced by Nani, while the excellent Jonny Evans missed out entirely due to fitness problems.
Such conservatism was a trait more commonly associated with Ferguson's opposite number Mancini until the start of the 2011-12 campaign, when the signings of Sergio Aguero and Samir Nasri helped to liberate City, allowing them to accumulate a positive goal difference of 60 prior to kick-off, six superior to United's.
Counter-intuitively, it was United who showed the greater endeavour in the opening stages, with Ferguson's side initially energetic and combative in midfield, even if an appeal for a penalty when a loose shot from Michael Carrick appeared to hit the arm of Kompany, placed across the defender's chest, was rather optimistic.
But as the half progressed, Wayne Rooney grew ever more isolated as an inhibited United became content to sit back and exploit opportunities on the break. City by contrast were more pro-active, but their probing passing moves too often broke down in the final third, the potent weapon of Aguero going largely unused.
City's first promising opening came after 16 minutes when the lively Nasri cut in from the right, negotiated his way past a couple of challenges and slipped in Tevez. The striker drove to the byline and cut the ball back for Aguero, but Phil Jones stuck a boot in to make a timely interception from the middle of the box.
A mildly rancorous subplot developed when Kompany was booked for a challenge on Rooney and the striker later became entangled with his opponent off the ball, but referee Andre Marriner had words with the two protagonists to calm matters in a first half that threatened to boil over at times, but only really simmered.
Though City increasingly came to exert control over the midfield and played the more artful football, their attempts to supply Aguero continued to prove faulty, the striker volleying wide after a corner was skewed into the air, firing another shot wide under pressure from Rio Ferdinand and then seeing an effort deflected past the post.
However, with United restricted to a wild effort from Park from a short corner, City pressed forward in the dying minutes of the half and won a corner of their own after Silva released Nasri with a glorious reverse pass and the Frenchman's cross was deflected behind.
Silva took the set-piece and picked out Kompany, who gave the culpable Chris Smalling the slip to leap and meet the ball in the centre of the box, powering his header close to David De Gea but past the United keeper for a 1-0 lead in first-half injury time.
United neglected to change their cautious approach at half time but after a further 10 minutes had elapsed, with City going close when Nasri curled an effort wide of the post, Ferguson was pressed into a substitution as Park was replaced by Welbeck, the change signifying an admission on the United manager's part that his initial tactics were faulty.
In a delayed response, City made their first change when removing Tevez, who had toiled without reward, for the midfield destroyer Nigel de Jong as Mancini sought to shut United down and hold on for an all-important victory.
De Jong brought his usual combative spirit to bear and a messy tackle on Welbeck quickly earned him a yellow card, as well as inspiring a heated confrontation between Mancini and Ferguson, who had to be pulled apart on the touchline. Carrick then flattened Nasri to earn a booking as tensions rose.
But still United were unable to test Joe Hart and City continued to dominate, Aguero thumping a shot into the side netting and the magnificent Yaya Toure collecting the ball on the halfway line, surging forward and bending a good effort just wide of the post.
In the closing stages, with United ostensibly the team desperate for a goal to hold onto top spot, it was City who possessed the greater potency and they should have won by a wider margin. Clichy was first denied by a fine stop from De Gea and then Nasri should have dispatched the ball from close range before getting the ball stuck under his feet having waltzed past two markers.
Even an unexpected five minutes of added time was not enough to rescue United, as they ceded top spot in highly disappointing fashion.