Shaun Squires went over to level the scores after eight minutes and, in the face of some outstanding Batley defence, Shaw’s penalty goal was all the Bulls could produce in response until Jake Mullaney bundled over with the seconds ticking down to half-time, making it 14-6 at the break.
However, the hosts refused to be deterred by the setback and they produced a remarkable second-half performance.
The Bulls clicked into action thereafter but were denied time after time by a determined Batley outfit and the home side extended their lead to five points with ten minutes to go, Cain Southernwood kicking a drop goal to add to his three conversions.
The former Bulls half-back then had the chance to kick his side seven points ahead on 73 minutes, but his penalty attempt drifted wide.
Danny Williams hauled the Bulls back into the tie just minutes later and Shaw showed unerring composure under pressure, converting from out wide to make it 20-19 to the visitors with five minutes left.
Chris Ulugia dived in on the hooter to round off the scoring, but Batley took the plaudits in a truly memorable game.
In a repeat of last year’s Grand Final, Rovers held a 6-4 lead at half-time thanks to Nathan Chappell’s converted try on 29 minutes after Liam Kay‘s early opener.
But the imperious Centurions scored 36 unanswered points after the break to extend their winning run to an incredible 15 matches.
Tom Armstrong and Tommy Goulden helped Leigh get 16-6 ahead after 54 minutes, but a devastating eight minute spell, which saw Kurt Haggerty and Michael Platt go over alongside another score from Armstrong, saw the Centurions go 24 points clear.
Winger Kay touched down for a second try on 77 minutes, already his tenth of the season, and Ryan Brierley notched a further score on the hooter to give the scoreline an even more convincing look.
In Cumbria, Whitehaven produced arguably the shock of the round, defeating London Broncos 18-16 at the Recreation Ground.
Haven, who came into the game winless, took the lead early on through Jordan Burns and held a 6-4 advantage at the break after Iliess Macani’s unconverted response for the Broncos.
James Newton made it 12-4 to the hosts on 48 minutes before John-Paul Brocklebank, who kicked three from three conversions, extended Haven’s advantage to 14 points with a try soon after.
The Broncos battled back with tries from Rhys Williams and Brad Dwyer leaving the margin at just two points with 18 minutes to go. But Haven produced a steely final quarter to hang on for a crucial first victory of the season.
The weekend’s only West Yorkshire derby saw Halifax run out 26-13 winners against Dewsbury Rams at The Shay.
The home side drew level when James Saltonstall went over on the hour, but Hyde edged the visitors back in front with a drop goal. However, Fax finished strongly and secured the win with late tries from Gareth Potts, Steve Tyrer and Luke Ambler.
Jimmy Watson went over on the hooter to give his side a 12-10 lead at the break, before Sanderson leveled the scores with a Penalty goal on 43 minutes.
But that was to be the last time the visitors troubled the scoreboard as the Hawks moved clear.
Kain ran in another on 54 minutes and completed his treble with ten minutes to go before Brad Brennan went over late on to help run up Hunslet’s highest score of the season.
The boot of Kyle Briggs was the only difference between Sheffield and Workington as the Eagles picked up a 14-12 win in Cumbria.
But Town hit back through Sam Forrester and Perry Whiteley, Carl Forber adding both goals, to make it 12-14 to the visitors on 75 minutes.
However, the South Yorkshire side clung on in the closing stages to earn a fourth consecutive win.