Tries from Delon Armitage and Rodd Penney secured a crucial bonus point for the home side, but Agen's strong finish - including tries from Sylvain Mirande and Luc Lafforgue - will be a concern for Brian Smith's men ahead of next weekend's return match at Stade Armandie.
In the final Challenge Cup game of the weekend, Border Reivers held on to beat 1997 European Cup champions Brive 25-22 at Netherdale.
Back row Andy Miller and centre Garry Law scored tries as the Scottish province took a 12-5 lead at half-time and the reliable boot of veteran former British and Irish Lion Gregor Townsend kept the home side ahead in the dying minutes.
Outside-half Martin Bottini scored his second try and his side's fourth of the match in the last minute to earn his side two bonus points.
Brive will be confident of overturning the result at Parc Municipal de Brive next weekend, although a spot as one of the leading runners-up looks like their best chance of making it to the quarter-finals given Newcastle's perfect record.