Hearts started the campaign 15 points adrift but have managed to reduce the gap between themselves and the Paisley side to nine.
A draw for Danny Lennon's side - at a ground where they have not won for almost six years - would ensure the points difference does not shrink any further going into the international break, but van Zanten insists that St Mirren will be on looking to claim their first victory of the season. He said: "We'll go there and try to win the game. Most weeks that is our aim, we never really talk about sitting in or trying to get a draw.
"Sometimes if you get a draw away from home you say, 'that was a good point' but I don't think we've ever gone into a game aiming to secure a draw. We always have the mentality that we believe we can win each game we go into and that won't change.
"Hearts will look at as a massive game as they'll be looking at us as a team that they can catch. If we could stretch our advantage to 12 points that would be huge psychologically. They've been trying to eat into that gap and we don't want them to eat into it any more. We've not played them this season so for the first time the gap is something we can control ourselves this weekend."
St Mirren head east having ended a run of five successive defeats with a 1-1 draw with Aberdeen. That offers Van Zanten encouragement. "We're going through a bad spell but Monday was our best performance of the season so we'll take a lot of positives from that. We want to be able to start looking up the table. We don't want to be worrying about what's happening at the bottom of the table. We want to pull away from that and start looking upwards. A win would help that."
Lennon opted to alter his defence against Aberdeen, with Van Zanten the sole survivor from the back four selected against Hibernian nine days before. The Irish right-back praised the contribution of Lee Mair, Darren McGregor and Sean Kelly for coming within six minutes of registering a first clean sheet of the term. "They were all excellent," he said. "Three changes to your back four isn't really heard of but, with suspensions and injuries, the manager was forced into it. I felt comfortable alongside the boys. I didn't see us conceding and Aberdeen even had a bit of luck with their goal. We were just disappointed not to get the clean sheet as the boys deserved it for their efforts."
Van Zanten singled out Mair for special praise following the 32 year-old's return to the team for the first time since May. He added: "Big Lee was outstanding when you consider it was his first appearance of the season. The level of the performance he put in says everything you need to know about him, his character and his attitude. It's been a tough time for him not being involved so to come in from the cold and put in a display like that was quite admirable. Even when he hasn't been involved he has kept himself fit and his attitude during training has been unbelievable. He was desperate to prove the manager wrong and I thought he was terrific."
While the experience of Mair was to St Mirren's benefit on Monday, an old head amid Hearts' squad of kids has been crucial. He might be just 27, but Jamie Hamill feels "like an old man" at Tynecastle, even if his recent displays have been far from tired, the combative midfielder guiding his younger team-mates through games.
Having been similarly helped by Gary Locke when he was emerging at Kilmarnock, Hamill is desperate to help his manager guide Hearts away from the foot of the table. "It's good to be floating about with the boys and the banter's good," he said. "That's really important given the situation we're in at the moment.
"On the pitch, I enjoy just getting in and about people and helping younger boys through the game. I had that as a young guy at Kilmarnock and it was of great benefit to me. I had the gaffer here, Gary Locke, when I was coming through; he was good, passing on different bits of wisdom. He's brought that to the Hearts dressing room, which is why everyone's pulling in the same direction.
"You can see in people if they've got it in their make-up to go on and do well as a manager and he certainly fitted into that category. He's handled everything that's been thrown at him in a difficult situation. Hopefully we can repay him at the end of the season."