After Jonny Bairstow (62) and Steven Patterson (40) added 91 for the ninth wicket to help Yorkshire progress from their overnight 327 for eight to 407 all out, Sidebottom dismissed England Twenty20 international batsmen Alex Hales and Michael Lumb for ducks.
That helped reduce the home side to 24 for two at lunch on the second day, still trailing the league leaders by 283 runs.
With second-placed Sussex not in action, third-placed Middlesex have the chance to put some daylight between themselves and their title challengers in the pursuit of Yorkshire and they were fighting back with the ball against bottom side Derbyshire on day three at Derby.
Middlesex conceded a first-innings deficit of 136 after being bowled out for 249 but their new-ball pace attack of Tim Murtagh and Steven Finn hauled the visitors back into the match by leaving Derbyshire on 20 for three in their second innings at lunch.
Murtagh sent back first-day centurion Wayne Madsen (two) and Ben Slater (nought) while England paceman Finn dismissed Chesney Hughes (three).
Another fast bowler released from the England squad this week also enjoyed some success with Chris Tremlett taking both wickets as fourth-placed Durham reached lunch on 82 for two on the first morning of their match with Surrey at Chester-le-Street.
Also in Division One, Warwickshire moved into the lead against relegation-battling Somerset after progressing from their overnight 283 for three to 353 for six at the interval, with Ateeq Javid still there on 133 not out.
Somerset did make three quick breakthroughs on the third morning though, including the wicket of second-day tormentor Laurie Evans for 138.
In Division Two, Worcestershire eased their way to 92 for two at lunch on the opening morning against Lancashire after being sent into bat by the leaders at New Road.
Second-placed Northamptonshire were frustrated by the weather as they sought to hammer home their advantage against Essex at Colchester.
No play was possible before lunch on day three due to rain, with Essex remaining on 187 for five in their reply to Northamptonshire's 531.
It was the same story at Canterbury where rain kept the teams off as Kent looked to continue their impressive first-day recovery against Gloucestershire, which saw the hosts hit back from a perilous 46 for three to reach a healthy-looking 334 for six at the close.
At Swansea, Murray Goodwin's unbeaten 66 helped Glamorgan to 153 for four at lunch in reply to Leicestershire's 203 all out.
- Sports & Recreation
- Michael Lumb
- Alex Hales