The West Lothian side are three points clear of the chasing pack in the Premier Division despite having just come up from the South League last season.
They had to dig deep to get the better of an Arniston side that restored some pride after their 9-0 defeat against Glenrothes the previous weekend.
And Pittman says the Broxburn fans will need to brace themselves to watch ugly wins now and again as his side bid for promotion two seasons running.
"I don't think we played as well as we can but this 3G surface encourages teams to play football, which is great to see," said the former East Fife and Partick Thistle defender.
"You've got to get the ball down and play it into your forwards on a park like this and most times this season we've been able to do that. The boys worked hard for this result.
"We might need to keep changing things away from home. The last two away games we've not played pretty football but got the results - and that's probably how we're going to have to do things."
Following the sacking of Brian McNaughton in the wake of that home hammering against Glenrothes, Max Christie and Steve Ellison took charge of Arniston for this game.
And, to their delight no doubt, the visitors were the better team in the first half of a clash that was certainly a good advert for the Junior game. Striker Lewis Coult hit the post with a header before seeing a goalbound shot turned behind by Broxburn keeper Gary Malley just before the break.
Pat Bonthrone also came close with a shot that flashed just wide.
Both keepers made excellent saves early in the second-half - Malley to deny Coult and Mark Weir to foil Chris Geddes at the other end - before the deadlock was broken in the 59th minute.
Blair Tolmie was adjudged to have handled the ball in the box, allowing Geddes to send Weir the wrong way from the spot. But Arniston hit back just three minutes later, Tolmie making amends with an excellent ball from wide on the right that picked out Coult, who sent a looping header over Malley.
That made it a test of Broxburn's character but they didn't panic and secured the points with two goals in relatively quick succession.
Geddes grabbed his second in the 75th minute, the little striker getting to a through ball from David Morrison just ahead of Weir to lift the ball over the keeper.
And, just eight minutes later, strike partner John Jeffrey punished the visitors for giving the ball away as he fired a shot into the corner of the net.
After being pushed up front to play as a makeshift striker after Coult had gone off, former Rangers defender Scott Nisbet pulled one back in the 89th minute with a superb lob.
But, within seconds, Broxburn scored a fourth goal, substitute Charlie Pearson hammering home a low drive after being put in by Shaun Martin.
"It's the usual," reflected Christie. "They've got the confidence of winning games and when that's the case the ball drops for you and you score scrappy goals.
"Whereas we had lots of clear-cut chances and were punished for not taking them, which is very frustrating." Nevertheless, there were plenty of encouraging signs for Arniston and, sensibly, none of the players carried out threats to stay away to show their displeasure over McNaughton having been axed.
"It was all a bit heated and emotional earlier in the week but the players are contracted to the club," added Christie.
"Everyone in that changing-room was brought to the club by Brian, myself included, and to see him going is a bit of a blow.
"Last week everyone at the club let themselves down so the first thing we had to get right was our discipline."
Broxburn Athletic: G Malley, Cairns, Gibson, Kiczynski, Ritchie, Nixon, Martin, Morris, Geddes, Jeffrey, Young. Subs: Wilson, Pearson, Heeps, Rycroft, Millar, Bruce.
Arniston Rangers: Weir, Lynch, Laird, Cunnison, Nisbet, Tolmie, McNaughton, McLennan, Coult, Morris, Bonthrone. Subs: Herd, Torrance, Oplika, Cennerazzo.
Referee: Ralph Gordon.
Broxburn Athletic 4
Arniston Rangers 2