Real Madrid have moved onto six points in Group H after recording a 3-1 victory against Borussia Dortmund in Tuesday night's Champions League fixture at Signal Iduna Park.

Cristiano Ronaldo hit a brace for the European champions, while Gareth Bale was also on the scoresheet as Real Madrid put their La Liga troubles to one side by posting their first ever victory away at Dortmund.

Dortmund boss Peter Bosz made three changes to the team that started against Borussia Monchengladbach in the league at the weekend. It was the same back five, but there were two changes in midfield as Gonzalo Castro and Nuri Sahin came in for Julian Weigl and Mahmoud Dahoud.

There was also an alteration in the front three as Andriy Yarmolenko was picked ahead of Christian Pulisic to start alongside Pierre-Emerick Aubameyang and Maximilian Philipp.

As for Real Madrid, it was the same back five that started against Alaves in La Liga at the weekend, with Marcelo's absence seeing Nacho continue at left-back. Luka Modric and Toni Kroos were back in the middle of the park, however, while Bale joined Isco and Ronaldo in the final third of the field.

Dortmund goalkeeper Roman Burki twice had to vacate his goal in the opening eight minutes to clear ahead of Ronaldo and Bale as Real Madrid managed to breach the home side's high defensive line.

Madrid had a wonderful chance to make the breakthrough in the 10th minute when Dani Carvajal broke into the Dortmund box, but instead of finding the unmarked Ronaldo, the right-back had a shot, and it was a comfortable save for the busy Burki between the home side's sticks.

Less than one minute later, the visitors had another clear opportunity as Ronaldo picked out the run of Bale with a brilliant pass, but Dortmund defender Lukasz Piszczek came from nowhere to make a goal-saving challenge.

There was then a huge moment of controversy in the 14th minute when Real Madrid captain Sergio Ramos appeared to clear a Philipp effort off the line with his hand, but the officials were not interested as the centre-back survived what would have been a spot kick and red card.

Instead, it was Real Madrid that made the breakthrough in the 18th minute when Bale produced a cushioned volley from a Carvajal cross as the reigning champions took the lead in Dortmund.

Bale had another opportunity in the 24th minute after breaking into the home side's box following a brilliant pass from Modric, but the Welshman could not beat Burki at his near post.

Aubameyang then had the chance to test Navas after finding space inside the Real Madrid box 10 minutes before the break, but the striker's first touch was poor, allowing Carvajal to come across and make the challenge.

It was the home side that dominated the ball in the latter stages of the first period, but Ronaldo twice came close to sending Real Madrid two goals ahead in the 44th minute, with his second effort just missing the post after a quick counter-attack, before Ramos headed a Kroos corner just wide in the final piece of action before the half-time whistle.

Dortmund came close to levelling early in the second half when Yarmolenko's header looked to be finding Aubameyang, who would have had a tap-in, but Raphael Varane came from nowhere to make a fine clearance.

Real Madrid doubled their lead in the 49th minute, however, when Bale raced down the left before delivering a low cross into Ronaldo, who simply could not pass up the opportunity to score on his 400th Los Blancos appearance.

Dortmund were back in the match just five minutes later though, with Aubameyang poking home a Castro cross from inside the Real Madrid box during an end-to-end period of the match.

Nacho had a decent chance to send Real Madrid 3-1 ahead just before the hour after meeting a corner from Kroos, but the Spaniard saw his effort stopped by Burki, who was well positioned to make the save.

Dahoud and Weigl both came off the Dortmund bench on the hour, and the change in formation made it even more of an open match as both teams continued to create chances on the counter-attack.

Aubameyang came close to scoring his second in the 67th minute after meeting a super pass from Gotze, but the Gabon international poked just wide of the post as Real Madrid survived another dangerous moment.

Isco then flashed one over the crossbar down the other end, before the Spaniard brought a wonderful save from Burki as the score remained 2-1 to the visitors entering the final 15 minutes of action.

Ronaldo secured all three points for the European champions in the 79th minute, however, when the number seven collected a brilliant pass from Modric before beating Burki at his near post as the Portuguese made it 94 Champions League goals in 90 matches for Real Madrid.

Marco Asensio and Ramos both tested Burki in the latter stages as Real Madrid threatened to score a fourth and fifth, but 3-1 was how it stayed as Dortmund lost their second Champions League game in succession.

Next up for Dortmund is Bundesliga clash against Augsburg on Saturday afternoon, while Real Madrid will continue their La Liga campaign with a home game against Espanyol on Sunday night.