Goals from Bernardo Silva and Thomas Lemar in the first 31 minutes of the game ensured a great start to the campaign for Leonardo Jardim's side.
On the other hand, Mauricio Pochettino's side will feel deflated with the defeat, especially after Toby Alderweireld's goal just before half-time looked like it was going to spring a comeback for the Lillywhites but it wasn't to be.
Spurs begin the game well but concede on the break
Despite a stop-start beginning to the game due to a couple of Monaco players getting injured, Spurs almost scored in the eighth minute when a lovely cross from Harry Kane found it's way to Son Heung-min in the box, who hit a first-time shot towards goal but it was blocked on the line by Monaco defender Andrea Raggi.
The home side took real heart from their start but a mistake from Erik Lamela, gave the ball away to Silva just outside the box. The midfielder gathered the ball and ran into the box making space for himself and he hit a fantastic shot into the back of the net to give the visitors a goal against the run of play.
The response from the hosts was positive to going a goal down but they were finding it very difficult to break down a very confident team who were showing why they had made a good start to the season.
Lemar scored Monaco's second but Alderweireld halved the deficit just before half-time
They showed this, even more, when they got a second goal just after the half-hour mark. Lemar, who came on as a substitute in the 5th minute, was first to the loose ball in the box to the smash the ball past Hugo Lloris into the top corner of the net.
The great thing though for the hosts is that they never let their heads drop as the continued to push forward to get a goal back before half-time.
The goal did finally come through a bullet header from Alderweireld as he rised highest in the box to head home an inswinging corner from Erik Lamela.
It was literally the last piece of action of a great first half at Wembley as both sides showed what they could do but the goal late in the half gave Spurs the momentum ahead of the second half.
The hosts were frustrated in the second half by some strong Monaco defending
This momentum did indeed carry into the beginning of the second half as the home side piled on the pressure to the visitors goal and they almost got back on level terms when a dipping shot from Dele Alli was heading into the net but for a fantastic save from Danijel Subašić.
Apart from this, though, the Spurs players found it really difficult to break down a very compact Monaco defence who blocked everything that was thrown in front of them.
This was until some fantastic hold up play from substitute Vincent Janssen found Kane in the box but the striker's shot was straight at Subasic when if he hit to either side of the keeper it would have been the equaliser.
Kane's miss turned out to be crucial as the hosts failed to create another chance in the final ten minutes of play to start their Champions League campaign with a defeat.