Nottinghamshire 285 (Montgomery 80, Hameed 70, James 50, Hogan 4-47, Harris 4-65) and 19 for 1 need another 436 runs to beat Glamorgan 318 and 421 for 5 (Byrom 144, Northeast 105*, Lloyd 60)
Notts start Thursday 19 for one after Haseeb Hameed’s wicket on day three. Byrom’s 144 was his second major century in three Championship matches.
Meanwhile Northeast, 105 not out, recorded his first hundred for Glamorgan, as David Lloyd and Billy Root both hit fifties.
Promotion challengers Glamorgan, the only side to defeat Nottinghamshire in this campaign, started the day leading by 86 runs and quickly pushed on as they posted only their second century opening stand of the season.
With Lloyd working hard to re-establish his red-ball form, Byrom reached his century just before lunch off 154 balls, a lofted straight six off Liam Patterson-White the highlight.
Notts finally got some reward in the over before lunch as Lloyd edged a drive off Brett Hutton to slip for 60 with the partnership worth 172.
Colin Ingram (33) and Byrom added 76 before Notts finally stemmed the flow as both fell in successive overs to Patterson-White.
Byrom’s innings, including 21 fours and with a healthy strike-rate of 70 runs per 100 balls, followed his recent 176 against Sussex to continue his solid start in a new role at the county.
However the stylish Northeast and busy Root made sure the punishment continued despite ultra-defensive tactics from the visitors in the final session, putting nine men on the boundary and bowling wide of the stumps.
Northeast added two sixes to his eight fours with his innings coming off just 137 balls, putting on 147 for the fifth wicket before Root (53) top-edged Luke Fletcher to Clarke.
Lloyd’s declaration challenged Notts to make their second highest run chase ever, and Michael Hogan claimed an early wicket as he bowled Hameed for one, beating his defensive shot.
Middlesex’s defeat at Worcester gives Glamorgan the incentive to go second in the table if they can force home their advantage at Sophia Gardens.