The wicketkeeper, brought out of impending retirement due to injury, added only one run to his overnight 84 to miss out on a maiden hundred for Yorkshire.
There was to be no first innings lead, Yorkshire adding only 28 runs for the loss of their last three wickets on the third morning to finish on 320 in reply to Somerset’s 399.
And, after Somerset scored 339-7 declared in their second innings, there was to be no serious prospect of a Yorkshire win, the hosts closing on 8-2 in pursuit of 419, heights they have never previously chased.
Instead, on a day when there was to be no joy for Yorkshire either in their pursuit of former England batsman Ben Duckett, who rejected them in favour of a Notts club for whom he could make his debut against them at Trent Bridge next week, there was only the stark detail that Somerset have driven this match from the moment that they fell to 5-2 after being sent into bat.
Since then, Yorkshire have been fighting valiantly but effectively playing a game of catch-up.
They would consider it a victory in itself, perhaps, if they could somehow materialise with a share of the spoils, which would not only ease their relegation plight but also put a big dent in Somerset’s fading title ambitions, further dimmed by leaders Surrey’s innings win over Notts at the Oval.
In glorious sunshine on the last day of August, there would have been no finer moment at Headingley this summer, or indeed a more popular centurion, had Hodd completed a three-figure score.
Brought back from the second team match at Taunton after Jonny Tattersall suffered a back spasm, he had played splendidly on the second day to rescue Yorkshire in tandem with Tom Kohler-Cadmore after the hosts had slipped to 119-5.
But after David Willey fell in the morning’s third over, taking a step down the pitch to pace bowler Josh Davey and edging a booming drive to first slip, Hodd went in the next over when he too picked out first slip as he tried to work Lewis Gregory to leg.
Hodd, who received a sympathetic hand as he left the field, has four first-class hundreds to his name, the highest an innings of 123 for Sussex against Yorkshire at Hove in 2007.
His highest score for Yorkshire remains the 96 not out that he made against Nottinghamshire at Scarborough in 2016, and, in a batting line-up that has struggled for runs, he must surely come into contention to play as a specialist batsman for the rest of the season assuming that the gloves revert to Tattersall.
After Willey’s dismissal had given Davey the first five-wicket haul of his career, the 28-year-old right-arm pace bowler finishing with 5-65 from 23 overs, Craig Overton rounded things off by having Jack Brooks caught at mid-on off a leading edge.
It left Somerset with a 79-run lead with just over an hour left until lunch, time enough for Yorkshire to reduce them to 28-3.
Willey bowled Ed Bryom with a ball that sent off stump flying, Matt Fisher – fit to bowl despite the recurrence of a toe problem suffered on the opening day –had Azhar Ali driving to cover, and Willey found Marcus Trescothick’s outside edge with Adam Lyth doing the rest at second slip.
Lyth’s part-time off-spin was responsible for the fourth wicket, but not until the fourth over before the tea break after a fine stand of 135 between James Hildreth and Tom Abell.
Hildreth, who scored 81 in the first innings, followed up with 72 before he was caught behind trying to chop through the offside.
The fourth-wicket pair also ran well, forcing mistakes with their aggressive intent on a day when Yorkshire’s fielding was not at its sharpest, the hosts twice conceding four overthrows.
After Steven Davies drove the fifth delivery after tea from Fisher to Lyth at slip, Abell and Lewis Gregory added 93 in 13 overs, Gregory thrashing 57 from 41 with three sixes before striking Willey to mid-on in the hunt for yet more rapid runs.
Abell reached his first hundred of the season from 147 balls and celebrated it with a leaping fist pump, going on to an undefeated 132 and declaring as soon as Josh Shaw ran out last man Craig Overton.
Gregory struck twice early in Yorkshire’s chase, bowling Harry Brook and having Lyth caught behind defending, to leave the hosts with a towering task.