Byron McGuigan went over for two tries

The Chiefs took the lead early on with a penalty by Steenson with Scott Wight levelling minutes later with his own three-pointer.

With Exeter having all the early possession Steenson edged them 6-3 ahead with another penalty.

The Chiefs were reduced to 14 players with Brett Sturgess yellow-carded for collapsing a rolling maul.

The Warriors went close after nice work from Tommy Seymour and Peter Murchie before Alex Dunbar put Byron McGuigan over for a score in the corner.

Scott Wight couldn't make the conversion from the touchline but the Warriors led 8-6 as Sturgess returned from the sin bin.

Steenson gave the Chiefs the lead with another penalty but he couldn't repeat that success after Glasgow replacement prop Jerry Yanuyanutawa went off his feet at a ruck.

Glasgow were exerting more pressure and they went ahead with Byron McGuigan grabbing his second try of the game after great play from the visiting pack created the overlap.

Scott Wight was successful with the extras to give Glasgow a 15-9 lead at the interval.

Glasgow made a strong start to the second period and after going close a couple of times Alex Dunbar crossed for the try. Scott Wight converted from in front of the post to stretch the Glasgow lead to 22-9.

The Chiefs tried to get back in the game and a good break from Tom James forced Glasgow's Henry Pyrgos to kill the ball. Steenson kicked the penalty to make it 22-12. With Pyrgos in the sin bin, Chris Cusiter came on for his first game after injury.

Exeter made their numerical advantage count when James went in at the posts. Steenson made no mistake with the conversion to bring the Chiefs within three points of the Warriors.

Glasgow emptied their bench and it paid off with James Eddie putting Mark Bennett in to score under the posts. Finn Russell's conversion made it 29-19 to the Warriors with eight minutes left on the clock.

Exeter pressed for the remainder of the match and managed to go over in the corner for a converted try but it wasn't enough to deny Glasgow the victory.

The teams will soon meet again, this time on more serious business, when Exeter visit Scotstoun on Heineken Cup duty in October.

"There were a lot of positive things out there," said Gregor Townsend after the game. "Our defence was really aggressive and they kept to their systems most of the time. In attack, we played some good rugby when we held our depth."