Swindon lead through Rory Fallon but Dean Windass, who himself is 36, levelled before Claridge hit a brace. Fallon pulled one back, but the Bantoms held on for a 3-2 victory.
Nottingham Forest threatened to win again, when they took the lead at leaders Swansea.
But Roberto Martinez equalised Jack Lester's strike, and boss Gary Megson opted to hold on for the point as he changed to a 4-5-1 formation.
The point keeps Swansea top of the table, though they are joined on 20 points by Huddersfield and Southend.
The Shrimpers triumphed in a dramatic win over Rotherham at Millmoor thanks to heroics from Wayne Gray.
They lead 2-0, but the Millers levelled before the break. Gray was sent on by boss Steve Tilson seven minutes from time, and had headed Southend into the lead within 60 seconds.
And he converted a penalty kick two minutes from time to seal the 4-2 win.
Huddersfield, perhaps feeling the effects of their Carling Cup trip to Blackburn in midweek, were held at Colchester.
George Elokobi headed the home side in front shortly after half-time, before substitute Gary Taylor-Fletcher replied in the 65th minute.
Doncaster's turnaround, kicked off by beating Scunthorpe last week and continued with a Carling Cup win over Manchester City, saw them run out 2-0 winners in their South Yorkshire derby at Barnsley.
Paul Green and Dave Mulligan scored the goals for Rovers, but their task was made easier by the Tykes' having Neil Auston and Antony Kay red carded.
Gary Johnson began his tenure as Bristol City in style, with a 3-2 win at Brentford.
Marcus Stewart, Luke Wilkshire and Steve Brooker were on target for the Robins.
His old club Yeovil beat Port Vale 1-0, with Matt Harrold hitting an 85th minute winner for the Glovers.
Oldham beat Bournemouth 1-0 at Boundary Park thanks to a penalty from Andy Liddell.
Jamie Burns grabbed the winner for Blackpool in a 3-2 win over bottom side MK Dons.
Chesterfield came from behind to beat Hartlepool 3-1, while Tranmere drew 2-2 with Gillingham.