And Yorkshire tightened their grip even further as Adil Rashid claimed two wickets in two balls late in the day for Durham to close on 54 for three, still trailing by 556 and requiring a further 407 to avoid the possibility of the follow-on.
South African left-hander Rudolph never gave a chance during his seven and-three-quarter-hour occupation of the crease and hit 35 fours from 389 balls.
Chris Woakes targeted Hampshire for the second time in less than a year as Warwickshire turned a crisis unto unexpected profit in their fluctuating contest at Edgbaston.
Having posted a maiden century with 131 not out at the Rose Bowl last July, Woakes improved on that with an unbeaten 136 in leading Warwickshire to a first-innings lead of 99. That represented a huge shift from a dire position on the second morning. The home side lost four wickets for five runs before the last three partnerships yielded 284 runs.
Darren Stevens's unbeaten century frustrated Lancashire against Kent at Old Trafford.
Replying to the home side's first-innings total of 320, Rob Key's batsmen had struggled to 97 for seven before Stevens' 92-run eighth-wicket partnership with Matt Coles. Stevens had made 101 not out by the time Kent were bowled out for 213.
Lancashire added 68 to their first-innings lead of 107 before bad light and rain ended play 15 overs early, but lost three wickets in the process.
Billy Godleman hit his first century for Essex on an absorbing second day of their match with Somerset at Taunton.
The former Middlesex batsman made 106, including 12 fours and three sixes, as his side reached 262 for five by the close in reply to Somerset's 387.
Pacemen James Harris and Jim Allenby picked up nine wickets between them to help power Glamorgan to a nine-wicket County Championship Division Two win over Worcestershire at New Road.
Harris grabbed five for 56 and Allenby four for 23 to dismiss the hosts for 171 and leave their side to score just 39 for a second victory of the season.
They wrapped up the resounding win inside two days to plunge woeful Worcestershire to their first defeat of the campaign after they lost their last six second-innings wickets for just 11 runs in 10.1 overs.
Centuries from captain Murray Goodwin and Rana Naved-ul-Hasan helped put Sussex on course for a fourth successive Championship victory.
The pair shared an eighth-wicket stand of 164 in 32.2 overs to help their side to 392 all out - a lead of 278 - on the second day against Leicestershire at Hove. The visitors closed on 226 for three in their second innings, held together by a unbeaten 68 from Paul Nixon, but still 52 runs behind.
Derbyshire pair Chris Rogers and Wayne Madsen notched a new record opening partnership of 273 against Northamptonshire as the visitors took complete control on day two at Wantage Road.
Skipper Rogers returned to haunt his former employers by notching an impressive 141 while South African right-hander Madsen ended the day unbeaten on 163.
Rogers and Madsen passed the previous Derbyshire best against Northants, 216, set by Alan Hill and John Wright back in 1979 as Derbyshire led at the close by 157 runs with eight wickets remaining.
Runs were again hard to come by at Lord's where 13 wickets fell and pace bowlers from Middlesex and Gloucestershire exchanged blows on day two.
Having been dismissed for 203 to trail the visitors by 95 on first innings, Middlesex rallied in the final two sessions of the day to reduce Gloucestershire to 139 for seven for an overall advantage of 204 runs.