Sale outscored Leeds by five tries to three, with Van Straaten slotting three conversions and two penalties to ensure a convincing win the home team.
They opened the scoring in the eighth minute with a try by former Wallaby Graeme Bond. Van Straaten missed the conversion, but his team had sounded their intentions early on.
Leeds, however, were in no mood to take second place and they took the lead in the 12th minute when Dan Scarbrough scored his team's first try and Duncan Hodge added the conversion.
But then things started to go wrong for the visitors. First Matt Salter was yellow-carded in the 26th minute and then Charlie Hodgson scored a try soon after, as the home exploited their numerical advantage. Van Straaten added the conversion for a 12-7 lead.
Four minutes later, with Tykes still down to 14 men, Matthew Cairns scored his team's third try. Even though Van Straaten missed his second conversion, Sale had raced into a 10-point lead.
This clearly gave them the confidence they needed and when Salter eventually returned to the playing field, he could do little to prevent Sale from increasing their lead.
A try by Steven Hanley in the 38th minute, with Van Straaten adding the conversion and a penalty two minutes later, saw the home team go into the break 27-7 up.
Try as they may, Tykes could not close the gap, especially not after Van Straaten added a 45th minute penalty to stretch that lead to 30-7.
Sale had Nick Walshe sin-binned in the 61st minute and that opened the gap for Leeds to finally score some second-half points. A try by Phil Christophers in the 63rd minute, along with Hodge's conversion made it 30-14.
But as soon as the home team was back to their full compliment of players they again stretched their lead – a Vaughan Going try and a Van Straaten conversion giving them a 37-14 lead.
Leeds scored a late consolation try, by Clive Stuart-Smith, which was converted by Hodge, but it was clearly a case of too little, too late by then.
For Sale Sharks:Tries: Bond, Hodgson, Cairns, Hanley, GoingCons: Van Straaten 3Pens: Van Straaten 2
For Leeds Tykes:Tries: Scarbrough, Christophers, Stuart-SmithCons: Hodge 3