Adebayor beat Jermaine Jenas to the ball after just four minutes at the Santiago Bernabeu Stadium to guide a header past goalkeeper Heurelho Gomes and through the legs of Luka Modric on the line.
Tottenham was left with 10 men from the 15th minute when Peter Crouch earned a second booking for a rash tackle.
Adebayor added Madrid's second by guiding Marcelo's cross home in the 57th minute before late goals from Angel Di Maria and Cristiano Ronaldo ensured a comfortable advantage before next week's return leg at White Hart Lane.
Ronaldo, Di Maria and Marcelo were rushed back from injury to start for Madrid.
William Gallas passed a fitness test to anchor Tottenham's back line with Gareth Bale starting on the left flank after recovering from a hamstring injury. Aaron Lennon was named in the starting XI, but was replaced just before kickoff by Jermaine Jenas. The speedy England winger's absence was noted as Spurs' attack disappeared behind Madrid's second half barrage.
Tottenham's first matchup against Madrid for 26 years started poorly as the north London club watched Ronaldo pepper its goal in the early stages before Di Maria's close shot was deflected for the corner from which Adebayor scored the opening goal.
Crouch was booked twice for a pair of reckless tackles deep inside Madrid's half - the England striker scything into Sergio Ramos in the eighth minute before later taking out Marcelo.
Madrid kept up the pressure while Tottenham looked to strike on the break. Rafael Van der Vaart - playing against his former team for the first time - missed a chance from inside the area in the 28th minute before Bale surged past Sergio Ramos to reach a long ball, but his shot past Iker Casillas sliced into the side netting.
Adebayor was guilty of a glaring miss in the 32nd as Ramos did well to head across goal toward the Togo striker from a difficult position.
Pepe took out Bale in the chase for a pass in the 36th minute for a yellow card that will see the Portugal defender miss the return leg.
Madrid coach Jose Mourinho couldn't have been happy as his side wasted much of its first-half possession, creating few decent scoring chances.
Van der Vaart was replaced by striker Jermain Defoe but Madrid controlled from the restart as it patiently tried to pick Spurs apart with Ronaldo putting a couple of chances wide.
Adebayor doubled the advantage when left alone inside the box and nearly had a third headed goal in the 66th, denied only by Gomes' quick reaction to tip over the crossbar.
Di Maria's individual effort made it 3-0 as the Argentina forward moved clear from Benoit Assou-Ekotto before unleashing a curling shot from outside the area beyond Gomes into the top corner.
Late substitute Kaka, returning from injury to play for the first time since February 26, also made his mark as the Brazil playmaker spotted Ronaldo at the far side with a cross that the Portugal international volleyed low past Gomes inside the near post for his fifth of the competition.
Nine-time champion Madrid has never been eliminated over two legs after a 4-0 opening win on home soil.
In the other match, Schalke swept to a stunning 5-2 victory over defending champion Inter Milan at San Siro.
Dejan Stankovic gave Inter the lead 29 seconds into the match, but Schalke levelled through Joel Matip. Diego Milito scored his first Champions League goal of the season to put Inter back in front, but Edu scored the first of his brace to bring Schalke level before halftime.
Inter nearly retook the lead soon after the break, but two goals in quick succession from Raul Gonzalez and an own goal from Andrea Ranocchia put the German side in total control.
Inter defender Cristian Chivu was sent off in the 62nd and with Inter's defense stretched to its limit, Edu added his second in the 75th.
The result was all the more remarkable given that Schalke was without key players Klaas Jan Huntelaar, Christoph Metzelder, Mario Gavranovic and Peer Kluge.
