While Barnsley were defeated 1-0 by Crawley Town at Oakwell on the opening day of the new season, Gary Johnson's Yeovil fell to a 3-0 home loss at the hands of Doncaster Rovers - another of those teams to drop from the Championship last term.
The results will have come as a blow to both sides as they bid to return to the second tier at the first time of asking, so they will be out to get some points on the board as they hit the road for the first time this weekend.
Barnsley travel to Crewe Alexandra on the back of a 2-0 League Cup first-round defeat to the same opposition in midweek.
The addition of former Swansea City and Reading man Leroy Lita to Danny Wilson's squad failed to have the desired impact on Tuesday, but the Barnsley boss remains confident his side can hit their stride soon.
"We'll get there," he told the club's official website. "Football-wise it's been good at times. We'll have to tighten up our defensive display.
"There's one thing we do know is that it will get better. In the meantime, we have to make sure if we aren't scoring goals that we aren't as loose."
Yeovil are in a similar situation to Barnsley as they visit Gillingham four days after hosting Peter Taylor's men at Huish Park in the League Cup - a match they lost 2-1.
Bristol City came out on top as two of the League One favourites went head to head on Saturday - winning 2-1 at Sheffield United - and host Colchester United as they aim to build a good run of league form, but defeat to Oxford United in the cup will have come as an unwelcome setback.
City's opening-day opponents, meanwhile, are at Sixfields to face Coventry City, who suffered a 3-2 defeat at Bradford City on Saturday thanks to a stoppage-time winner from James Hanson.
Chesterfield began life in League One with a 2-1 win at last season's losing play-off finalists Leyton Orient and welcome fellow promoted side Rochdale to the Proact Stadium in the second round of fixtures. Orient are at Oldham Athletic on Saturday.
Crawley welcome Swindon Town to Broadfield Stadium as they aim to follow up their win over Barnsley, while Peterborough United and MK Dons meet at London Road.
Elsewhere, Doncaster Rovers host Port Vale, Fleetwood Town travel to Notts County, Scunthorpe United are at home to Preston North End and Walsall welcome Bradford City.
