Dyson will deny the Spaniard a place in Colin Montgomerie's side if he wins and Jiménez is outside the top nine, and his birdies at the second and seventh put him only one off the lead.
However, Dyson then three-putted the short tenth and with Jiménez coming back from a bogey on the 239 yard fourth by picking up shots at the sixth and ninth they were both seven under par and joint ninth.
Things were so tight at the top, however, that it was all to play for.
England's Gary Boyd, who lost a play-off for the Czech Open last Sunday, and Irishman Damien McGrane led at nine under.
No fewer than six players were only one behind and they included Italian Edoardo Molinari, determined to impress Montgomerie as he deliberates over the three wild cards he will hand out on Sunday night.
Barclays Scottish Open champion Molinari, playing with Dyson, even shared top spot after an outward 33, but he was bunkered on the tenth and also bogeyed.
When Boyd also three-putted the tenth there was a five-way tie for the lead with Edoardo Molinari, Stephen Gallacher, Oliver Wilson and Gregory Bourdy - and no fewer than eight players had had at least a share of top spot on the day.
Dyson was again only one behind and his Ryder Cup chances were boosted when Jiménez bogeyed the 11th, 12th and 13th and plunged to 27th.
When Edoardo Molinari made a 25 footer on the 16th and his brother birdied the 14th they were joint leaders at nine under - with Dyson among those only one back after he chipped to three feet for a four at the 16th.
|T3||JIMÉNEZ, Miguel Angel||ESP||18||-7|