Sjoeke Nuesken and Guro Reiten gave Chelsea the lead before Alba Redondo pulled one back for the visitors before half-time.

Mayra Ramirez struck in the second half to restore Chelsea's two-goal advantage. A late Linda Caicedo tap-in set up a nervy finale at Stamford Bridge.

Chelsea went into the lead in the second minute when Johanna Rytting Kaneryd's cross struck the unfortunate Sheila Garcia, via the head of Nuesken, and trickled into the Madrid net.

The English champions doubled their lead shortly before the half-hour as the referee pointed to the spot after Maria Mendez caught Nuesken as the pair fought over a loose ball in the box.

Reiten slotted the spot-kick beyond the reach of Misa Rodriguez, who had correctly guessed which way to dive.

Madrid halved the deficit on 39 minutes. Fine wing play by Olga Carmona created the chance and after some pinball in the Chelsea box, Redondo showed composure to take a touch and finish from 10 yards.

Ramirez restored the hosts' two-goal lead eight minutes into the second half with a header that looped over goalkeeper Misa.

Caicedo converted from close range in the 84th minute after Lucy Bronze had blocked a goal-bound effort on the line, however the Spaniards were unable to complete the comeback as Chelsea ground out the win.

Also in Group B, Dutch club Twente beat Celtic 2-0 in Glasgow thanks to a Kayleigh van Dooren brace either side of the interval.

Earlier, a trio of headers from Kadidiatou Diani, who scored twice, and Vanessa Gilles gave last year's beaten finalists Lyon a 3-0 home victory over Galatasaray.

France attacker Diani opened the scoring when she stole in to nod home a Tabitha Chawinga cross with 34 minutes on the clock.

Chawinga then got her second assist of the match -- and Lyon scored their second goal -- right on the stroke of half-time as Gilles turned in her chipped cross from close range.

Gilles went close with another header early in the second period, but her towering effort from a corner rattled against the crossbar.

Diani did make it three in the 77th minute, her guided header crept inside the far post after Amel Majri had burst down the left flank and drilled in a cross.

"They had a lot of fight and it's never easy to combat that, but that's football and that's the Champions League. We're so happy to come away with the win," said Lyon defender Gilles.

In the Italian capital, a 14th-minute penalty converted by new captain Manuela Giugliano was enough for Roma to upset two-time champions Wolfsburg 1-0.

The visitors struck the woodwork twice after the break but were left frustrated as Roma held on to take all three points and go second in Group A -- behind Lyon on goal difference.

On Wednesday, Arsenal visit Bayern Munich and Champions League holders Barcelona start their title defence at Manchester City.