NICOSIA, Oct 1 (Reuters) - Bayer Leverkusen secured their first points in Champions League Group F on Tuesday, beating Maccabi Haifa 2-0 in Nicosia.

Goals from Croatian Marko Babic in the 31st and 64th minutes did the damage as Haifa struggled for most of the match.

Haifa's woes were compounded as Avishai Zano missed a penalty in the 44th minute when his spot kick hit the post and he then blasted the rebound high into the stands.

Haifa coach Yitzhak Shum threw caution to the winds after the second goal and brought on three attacking players. But the ploy failed as the Germans held on.

Haifa were unable to reproduce the same intensity as they did in their 3-0 home win against Olympiakos a week earlier.

The Germans were the more dangerous and held the majority of possession, although untidy finishing let them down on occasions.

Babic put Bayer in front with a glancing header from a free kick on the right by Bernd Schneider.

His second was a long shot which evaded the advancing keeper and ended up in the top corner of the net.

In the group standings, Bayer join Olympiakos and Haifa on three points, six behind runaway leaders Manchester United.

'It wasn't an easy game at all, Maccabi played very well, but they looked a little tired,' Leverkusen coach Klaus Topmoeller said.

'We are very happy to win this. It's in our grasp to advance with two home games in hand.'

Shum said: 'We created chances to score that we didn't manage to convert and we conceded two goals. That's the only difference between us and Bayer Leverkusen.'