Real Madrid and Manchester City qualified for the Champions League knockout rounds with victories over Paris Saint-Germain and Sevilla respectively Tuesday. And there was relief at Old Trafford as Manchester United ended a 404-minute wait for a goal to beat CSKA Moscow 1-0. A fortuitous goal from Nacho proved decisive for 10-time champion Real to win 1-0 despite being outplayed for the majority of the first half of their Group A game at the Santiago Bernabeu. PSG was on top throughout the first period but Adrien Rabiot's volley cannoned back off the foot of the post and Edinson Cavani squandered a great chance when left with just goalkeeper Keylor Navas to beat. And when Toni Kroos let fly from distance just after the half hour, the ball spooned up off Thiago Silva and fell to Nacho — who had only come on for injured left-back Marcelo two minutes earlier — inside the area. PSG goalkeeper Kevin Trapp initially came for the looping ball but as he backtracked from no-man's land, Nacho's casual side-foot spun wickedly on the bounce and dropped inside the far post. Little happened in the second half but Angel Di Maria did hit the bar late on with a free-kick, although the French champion couldn't find the goal their play deserved. Real qualified from Group A, thanks to Shakhtar Donetsk romping to a 4-0 win over Malmo, a result which means a win for PSG in either of their last two matches will ensure it joins Real in the last 16. City banished memories of its recent Champions League struggles as a confident 3-1 win in Seville qualified it for the last 16 with two games to spare in Group D. Borussia Moenchengladbach's failure to beat Juventus in Germany, where the sides played out a 1-1 draw, meant City, which now tops the group, has made it to the knockout stages for only the third time. Raheem Sterling set it on its way with a goal after eight minutes while Fernandinho doubled the advantage three minutes later. Frenchman Benoit Tremoulinas gave the Spanish host hope but Wilfried Bony's crisp low finish nine minutes from the break effectively killed the contest, giving City a third straight Group D victory. In Germany, Fabian Johnson gave Borussia the lead on 18 minutes but Stephan Lichtsteiner marked his return from minor heart surgery with the equalizer a minute before the break to restore parity. Juve held on for the final 35 minutes with 10 men after Hernanes was dismissed for a late tackle on Alvaro Dominguez, meaning the Italians need only two more points to go through. City's neighbor United labored for long periods against CSKA at Old Trafford before a late Wayne Rooney header snatched a 1-0 win that puts the Red Devils in control of Group B. PSV Eindhoven's 2-0 win at home to Wolfsburg means United lead those two by a point but a victory over the Dutch outfit at Old Trafford in three weeks' time will book its place in the last 16. Rooney's goal saw him equal Denis Law in second on United's all-time scorers' list with 237 goals. United came into the game on the back of three successive 0-0 draws with manager Louis van Gaal's tactics increasingly coming in for criticism. Just before Rooney scored, goalkeeper David De Gea, a virtual spectator throughout, had to come to his side's rescue after Ahmed Musa's perfectly-weighted ball sent Seydou Doumbia racing clear. De Gea made a brilliant one-handed save to deny the Ivory Coast forward before the back-tracking Chris Smalling slid in to crucially clear the follow-up off the line. Almost immediately, Untied went up the other end, carved CSKA open and Rooney headed in Jesse Lingard's cross unmarked from seven yards. Benfica is close to qualifying from Group C after beating Galatasaray 2-1 in Lisbon, while Atletico Madrid was held 0-0 by Astana in Kazakhstan, although the Spaniards are second and three points ahead of Gala.