In a game of few chances, the game was settled by a penalty kick from Rodriguez that really shouldn't have been given in the first place by the referee.
The controversial spot-kick now gives the visitors a big advantage going into the second leg in Basel on Sunday evening.
After a bright start from the hosts, the visitors controlled the first half
The game started with the hosts starting on the front foot and looking like they could cause the visitors a lot of problems but after a brief spell, the visitors took control of the game.
From this, they created a couple of big chances that they could easily have scored from. The first one came after a good passage of play which ended with Granit Xhaka putting a good shot over the bar from the edge of the box.
The second big chance came when a great pass from into the box from Xherdan Shaqiri found Haris Seferović but his first-time volley was brilliantly saved by Michael McGovern.
Apart from these big two chances and even though they had all of the possession, the visitors found it difficult to break through a stubborn home defence and at the break the scoreline remained goalless.
The visitors continued to dominate at the start of the second half
It was more the same at the start of the second half as the visitors continued to show their dominance as Shaqiri came very close to getting the opening goal when a cross from Rodriguez found the winger but his curling shot went just over the bar with the keeper beaten.
Rodriguez netted from the spot after a controversial award from the referee
The visitors though didn't have long to wait for an opening goal as the referee gave them a penalty after a volley from Shaqiri hit Corry Evans and referee Ovidiu Hategan pointed to the spot for handball much to the surprise of all the home players.
Rodriguez was the man to step up to take the penalty and he calmly sent McGovern the wrong way to give the visitors the crucial breakthrough in the game.
Magennis should have equalised for the hosts as the visitors head into the second leg with the advantage
The goal really hit the home side hard as it took them a while to respond but they should have got an equaliser when a great free-kick from Chris Brunt found Josh Magennis unmarked in the box but the striker put his header wide when he should have scored.
The home side really tried to find an equaliser before the end of the game but they failed to create any more clear chances and they almost got caught on the break a few times but last-ditch tackles meant the game only ended 1-0 to the visitors.
Therefore, the game ended with the visitors coming away with a key advantage ahead of the second leg in Basel on Sunday evening.