Australia finished the day on 200 for six in their second innings and with a healthy lead of 310 runs in a match that they only need to draw to take the series having won the opening Test.
Cowan believes that Australia should go on to wrap it up in style.
"I think we're in control, definitely. I think 300 already is a big score.
"Fifty on a wicket like that can be as good as a hundred. Sure the runs don't show on the scorebook but over 300 to chase is a helluva lot of runs."
West Indies had looked to have got back into the match having added some important runs in the morning session before being bowled out for 218 and then took two quick wickets with David Warner going just before lunch and the dangerous Shane Watson just after the resumption.
The hosts total owed much as ever to a typically stubborn innings of 68 by veteran Shivnarine Chanderpaul.
West Indies had been 165 for eight overnight with Chanderpaul and Ravi Rampaul having already put on 45 for the ninth wicket.
They took their partnership to 66 before Nathan Lyon broke through.
Rampaul came down the wicket but got a thick outside edge and the ball flew up to Warner at point.
The visitors took the new ball after 83.1 overs and in the end it was Chanderpaul that fell.
Mitchell Starc was bringing the ball back in off the seam and one finally got past the obstinate West Indian's bat and trapped him lbw.
Chanderpaul's 68 makes him the highest scorer in a low scoring series with 277 runs at an average of 92.33.
It left Australia to face a tricky five overs before lunch and the West Indies got the breakthrough that they would have wanted.
Warner had already struck Rampaul for two boundaries. However, in the last over before the interval he drove loosely at a Kemar Roach delivery and edged to the only fielder in the slip cordon, Chanderpaul.
Shane Shillingford, who had taken six wickets in the first innings, came on to bowl straight after lunch.
In his second over he found the edge of Cowan's bat but Carlton Baugh, who has had a poor series behind the stumps, put down the knee-high chance.
In his next over, though, Shillingford struck.
Watson guided a ball off the face of the bat straight to leg slip where Darren Sammy held on to a sharp chance and the tourists were looking shaky at 25-2.
Cowan and Ponting settled and started to build a useful partnership with the former bringing up his third test half century with a cut through point.
However, once again he failed to build on a good base and was out for 55 as he got a thick edge to a Marsingh Deonarine delivery and the ball flew at shoulder height to Sammy at slip who took a terrific catch.
Ponting took another risky single to bring up his fifty, also his first half-century of the series.
Shortly afterwards his luck ran out. He had made 57 when he ducked under a Roach bouncer but had left his bat sticking up like a periscope.
The ball hit it and looped up for Chanderpaul to scoot around from slip and take the catch.
Cowan hadn't witnessed such a dismissal before.
"Unbelievable, I guess if you play cricket long enough you are going to be dismissed every which way, I guess he was due for a periscope," said Cowan.
"I feel sorry for the bloke because he has been batting beautifully and again it will give ammunition to some bloody journalist back home.
"Ammunition to lampoon, but you guys have seen how well he is playing in tough conditions but what a bizarre dismissal, but I guess you can only shrug your shoulders and say ‘that's the game'."
Shillingford slowed Australia's progress when he had Michael Clarke caught by Darren Bravo and first innings centurion Matthew Wade fell for just four this time round trapped lbw by Deonarine.
The West Indian all-rounder knows that it's going to be tough for his team to get the win it needs.
"Whatever Australia put on the board we have to go there and look to get it," he said.
"The first thing is to try and get those four wickets for as low as possible tomorrow morning and when the time comes to bat you're just going to have to fight very hard because the pitch is not conducive to strokeplay as we've seen.
"Everybody will have to dig in there, score some runs and hopefully when we get a chance to bat again we just knock off the runs"