After a goalless first half Jed Phillips nodded the Ambers in front on 61 minutes, then added a second four minutes later by converting a Jamie Green cross.
Cameron Rigby opening his Handsworth account with a neat far post finish in the final minute before Brad Lovell netted Penistone’s consolation in stoppage time.
Ambers boss Jas Colliver said: "Delighted to get off to a positive start, I’m sure a lot of people looked at the fixture and thought it could go either way.
"I felt in the second half we dominated and thought we were deserved winners, we hit the woodwork twice and limited Penistone to only a few chances.”
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Church manager Ian Richards added: "Obviously it was not the opening day result we wanted. We’re disappointed to lose but we’ll put it right. We lost to the better team and one of the title favourites but we’re only three points behind the teams that won so it's not a disaster.”
Hallam made a dream start to the season with a thumping 7-0 win at ten-man FC Bolsover as they look to end their eight-year Premier Division exile.
Ben Thornton hit a hat-trick with new singing Reece Treasure bagging a couple to have Hallam in complete control just past the hour mark with Bolsover already down to ten men. Sam Smith's deflected shot made it six with substitute James Steer completing the scoring, poking home from close range in the final minute.
“It was a great way for us to open our campaign,” said joint manager Steven Whitehead.
Worksop Town got off to a winning start with an excellent 2-1 victory at relegated Goole AFC.
Tigers skipper Jamie Price led by example smashing home the opener on 37 minutes after a corner had only been half cleared. The home side hit back quickly when just three minutes later Adam Lund volleyed home from a corner.
Worksop’s winner arrived just past the hour mark. Steve Woolley with a drop of the shoulder and a run into the box unleashed a left foot drive that took a slight deflection off substitute Kyle Jordan before nestling in the bottom corner.
Danny Frost scored twice on his league debut as Maltby Main beat Harrogate RA 2-0 at Muglet Lane.
Staveley MW had to settle for a point from a 1-1 draw against Barton Town at Inkersall Road. Adam Baskerville had given the Trojans a 20th minute lead after latching onto Connor Williamson’s exquisite throughball, only for the visitors to grab an equaliser seven minutes from time.
Athersley Recreation went down 3-1 against Liversedge where Lee Garside netted a stoppage time consolation .
Parkgate started life in Division One with a 3-0 home defeat against fancied Nostell MW at Green Lane.
Jack Owen gave the visitors the lead inside the first 15 minutes before ex-Parkgate players Danny Citchlow (47) and Brad Kerry in injury-time wrapped up the the three-points.
Dronfield Town and Swallownest both suffered opening day 2-0 defeats against Campion and Winterton Rangers respectively.
Worsbrough BA put last season's struggles behind them as Lee Morris’ side made a flying start with a 2-0 victory at league new-boys Harworth Colliery
Kieran Hirst and Joe Dungworth had the Briggers 2-0 up before Harworth got one back through Mark West's 89th header to make it a tense finish.
AFC Emley won 2-1 at Armthorpe Welfare despite having Dan Stocker sent off at the start of the second half. The Pewits were already leading 2-0 at the time through a Ruben Jerome header and Shane Hamilton three minutes from the interval.
Welfare got one back four minutes from time when Luke Williams netted a low drive but the visitors held on to take the three points.
Rossington Main had to settle for a point from a 1-1 home draw against Ollerton Town after Lee Holmes had headed them into a 20th minute lead.
Fixtures, Tuesday: Division One: Dronfield Town v Rossington Main,
Wednesday: Division One: AFC Emley v Selby Town, Grimsby Borough v FC Bolsover, Nostell MW v Harworth Colliery, Worsbrough BA v Campion.