The £4million recruit from Burnley took just two minutes to register his first Hoops goal on his full debut as he diverted Jermaine Jenas' shot past Exeter goalkeeper Artur Krysiak.
Danny Simpson wrapped up the win with the second goal five minutes into the second half, but it was the performance of Austin that had Jordan drooling.
"It's great for him," Jordan said. "I think he will be pleased with that and he showed that he is not just a good goalscorer because he made some good runs as well.
"He ran the channels, held the ball up and played well with Bobby Zamora and Andy Johnson, so it bodes well.
"It's a huge weight to get off your shoulders by scoring on your debut. When you come to a new club, you want to get a goal as soon as you possibly can and he scored inside two minutes. He will score goals."
Rangers were worthy winners at St James' Park as Exeter rarely troubled goalkeeper Brian Murphy.
The closest they came was when substitute Arron Davies rattled the crossbar, while Shaun Wright-Phillips almost added a brilliant third for Rangers, but he too was denied by the woodwork.
"We got the goal and it could have been more in that first half-hour," Jordan added. "We played all the football, created all the chances and we should have put the game to bed.
"At 1-0, it is never over and we have found that to our cost in the past.
"The second goal was very important because they came into it a little bit and we rode our luck for 10 minutes, but I think we were quite comfortable overall."
Exeter manager Paul Tisdale cut a frustrated figure at full-time.
He said: "I expected more to be honest,. I don't think we did as well as we could have done.
"I think we could have performed better in the first half. I asked the players to play a certain way, but we didn't show enough energy, except for Liam Sercombe, who looked like he should have been playing for them.
"Maybe it's because we have had two games at the start of the season and we're not quite up and running yet.
"We improved in the second half and the substitutions gave us a lift, which is what I intended it to do.
"I was hoping we would have been a goal in it at that point, I wanted to be in a position where we had a chance, but at 2-0, I think it was just too much to ask for."