Wilson said the visitors shook them up a fair bit in the first half and they were lucky to go to halftime 1-0 up.
Josh Stevenson drew first blood in the 14th minute after English import centre-mid Ryan Tinsley lunged just outside the far post to nod the ball back into play from a freekick for the midfielder to head it into the net.
"But we came out in the second half and put the game to bed with a 3-0 lead."
Three minutes after the break, Rovers wing back Phil Dol pushed a pass through to Stevenson who turned the ball around an advancing Tawa keeper Lance Ramaekars before drilling it into the net from just inside the 18m box for a 2-0 lead.
A minute later, Welsh import Miles John floated a cross from near the corner flag.
The ball clipped Tawa centreback James Sharp on the leg before curling into the goal for a 3-0 lead.
Wilson couldn't put his finger on why they started lethargically but figured teams had those days.
"You just have to weather the storm, claw your way back again so we did that today and I'm happy."
It's three wins out of four for the Rovers and an unblemished record at the Bluewater Stadium this season.
"We are three points from the top of the table so we'll take that and then we have [Wellington] Olympic away next weekend," Wilson said.
The Rovers play Taradale AFC in an away Chatham Cup knockout match after that and then host Wairarapa United at home.
"It's a hard run in now but we're getting there with Bill pulling us together to play the right kind of football to do well," he said of coach Bill Robertson before lauding Stevenson's nose for sniffing out the net.
Tawa striker Todd Painter butchered a goal in the 17th minute from about 8m in front of the goal after a deft pass from youngster Richard Bott.
A crisp finish would have served him better but the blast hit the upright and deflected into play. Lookout for Bott who has all the individual attributes of a talented footballer but needs to understand the concept of cohesiveness that makes a team tick and also cultivate a voracious appetite for scoring goals.
Two minutes later Ramekars thwarted Wilson's pile driver.
Bott had another chance in the 27th minute when he took a touch and drove from inside the 18m box but the ball grazed the bottom of the crossbar and jagged down in Rovers' favour.
In the 32nd minute, Tawa had another chance from a goalmouth melee but midfielder Oli Chapman's foot worked like garlic to vampires.
The visitors made a blunder in the 51st minute with an ill-timed back pass but keeper Ramaekars ran out of his sanctuary to dispossess Angus Kilkolly.
Chapman botched a goal in the 62nd minute after Stu Wilson ran down the flank to curl a well-timed cross but instead of taking a touch the midfielder rocketed it way above the crossbar from point-blank range.
It got bad to worse for Sharp in the 68th minute when he hacked down Stevenson, albeit with no malicious intent, to leave the field for his second yellow card.
In the 85th minute, substitute Abe McPherson lasted only a few minutes after what appeared to be a sprig-baring tackle on Dol who had to be stretchered off with an ankle injury.
On resumption Tawa centre-mid Karl Romijn latched on to a botched clearance from centreback Danny Wilson to drill the ball above Rovers keeper Jonty Underhill caught on the hop closer to the edge of the 18m box for a 3-1 score.
Wood rued the missed chances.
"It was a bit of bad luck but you have to take those opportunities so in the end it came back to haunt us."
Wood felt the Rovers were daunting in set pieces but overall Tawa managed them well.
He felt the first yellow card on Sharp was disappointing but the second justified.
However, he was too far from McPherson to pass fair judgment but accepted the ref's decision.
"At the end of the day you make a challenge with your sprigs up and if you get it right you're all right but if you don't then you pay the penalty."
Tawa lost 1-0 last season with a man sent off early.
