The Reds gave it everything in north London, and applied significant pressure on the Spurs goal in both halves, but could not find the equaliser that they arguably deserved on the balance of general play.
The decisive moment of the contest came in the 13th minute, when Maddison was first to the rebound from Lucas Bergvall's low shot, which had been parried by Andre Onana.
Both sides had plenty of chances during the remainder of an at-times frantic encounter that could easily have ended 3-3, but Ruben Amorim's Reds were left ruing a lack of ruthlessness in the Spurs penalty area.
There was, at least, one bright moment in the final stages, however, when 17-year-old Chido Obi came on for his first-team debut.
FIRST HALF – A MISSED OPPORTUNITY
Despite a strong, possession-heavy start to the game for Spurs, United had the better of an entertaining first half.
Rasmus Hojlund shot straight at Guglielmo Vicario when sent clear by Harry Maguire's long pass and, from the loose ball, Alejandro Garnacho tested the Tottenham keeper again with a curler targeted at the top corner. Then Ben Davies cleared Diogo Dalot's resulting cross, from just in front of the goal line.
But it was the hosts who took the lead in the 13th minute, when Bergvall's low left-footed drive was palmed away by Onana. Maddison reacted quickest, and was rewarded with a simple chance to prod the ball home. One-nil.
United responded decently enough. Joshua Zirkzee shot from distance and only narrowly failed to find the bottom corner, but by far the best chance of the first 45 fell to Garnacho, who was well located around 10 yards out by Bruno Fernandes's simple pass. Sadly, the Argentina international skied his shot, when most inside the stadium expected an equaliser.
Mathys Tel had an effort saved comfortably by Onana shortly after, and both sides enjoyed moments of promise during the remainder of the half. But United headed to the dressing rooms behind, and surely destined for pleas from the coaching staff to be more ruthless, more clinical, in the final third.
SECOND HALF – TO AND FRO
United had peppered the opposition goal during spells in the first half, and they had plenty of other promising phases in the second 45. The only problem? Spurs looked equally dangerous, and already possessed that all-important advantage, courtesy of Maddison's opener.
Tel had the first chance after the interval, but could only shoot tamely at Onana, and then came the Reds' best period of the game, between the 55 and 60-minute marks. Garnacho was sent racing clear behind Spurs' high line, but was denied by Vicario and then, off balance, unable to turn the rebound towards Hojlund. Minutes later, the same player had a low drive which was again well repelled by the Spurs stopper, whose sight line was possibly obscured by Zirkzee, standing in an offside position.
The Dutchman was the recipient of possibly our best chance of the entire second half when he latched on to Noussair Mazraoui's dangerous cross from the right, but could not angle the ball inside the far corner. Despite that disappointment, it was one of the forward's better performances for the Reds this season, with plenty of nice touches and intelligent play. The former Bologna man will just be disappointed that he did not find the goal required to level the game.