Robinson turned in Joe Thompson's cross in the 12th minute, then fired home a free-kick seven minutes later to put Tranmere in charge.
His hat-trick came in the 66th minute with another free-kick.
Tranmere are one of only three teams with a 100 per cent record after the second round of matches.
Chris Brown's late goal gave Doncaster a 2-1 win over 10-man Bury as they came from behind.
Bury led after only five minutes when Joe Skarz headed in from a corner, but some great link-up play with Billy Paynter allowed Kyle Bennett to fire in the equaliser nine minutes before the break.
Bury then had Steven Schumacher dismissed for bringing down Brown in the 68th minute, and he punished them six minutes from time by firing in the winner.
Goals in either half from Francois Zoko and Neal Bishop, the second a fine strike on the turn, gave Notts County a 2-0 win over Hartlepool.
Sheffield United bossed their game away to Coventry, but fell behind to Stephen Elliott's counter-attacking goal just after the hour, and had to settle for a 1-1 draw thanks to Nick Blackman's 84th-minute equaliser.
Swindon got their first win as they cruised past Crawley 3-0, enjoying a little luck along the way.
Matt Ritchie's opener was intended as a cross but floated into the far corner of the net and Swindon survived a series of chances for Crawley before Tommy Miller fired in a second and Raffaele De Vita smashed in a third from close range.
Late goals gave Yeovil their first win as they beat Brentford 3-1 away from home.
James Hayter got Yeovil's first after 23 minutes, but Clayton Donaldson levelled before Hayter restored the visitors' advantage 10 minutes from time.
The unfortunate Tony Craig then scored an own goal to make sure of the points for Yeovil.
MK Dons had a man sent off for a third straight game as Alan Smith collected another red card, but they seem to be getting used to playing a man down and still took a 1-1 draw at Bournemouth, with Daniel Powell cancelling out Lewis Grabban's close-range opener.
There were late goals for both teams as Portsmouth got a 2-2 draw away to Colchester.
Portsmouth led after half an hour when Luke Rodgers slid the ball home from Liam Walker's throughball, but Michael Rose's outstanding 30-yard half-volley levelled it before the break.
Magnus Okuonghae thought he had won it for Colchester when he turned in a corner seven minutes from time but Jordan Obita rescued a point for Pompey.
Paul Parry's 20-yard effort in only the fourth minute was enough for Shrewsbury to see off Preston 1-0.
Lucas Akins got the only goal as Stevenage won 1-0 away to Leyton Orient - the only team other than the Iron to have lost both their opening games.
George Bowerman scored in the 79th minute to cancel out Youssouf M'changama's opener as Walsall salvaged a 1-1 draw at Oldham.