A goal&nbsp;in each half helped Huddersfield to three points in Paul Tisdale's 300th game in charge of the Grecians.
Simon Grayson took charge of the home side for the first time since replacing Lee Clark and&nbsp;despite&nbsp;chances for David Noble, Jake Taylor and Dan Nardiello&nbsp;they took the lead five minutes before half time thanks to Jamie McCombe's header.
And the hard-working Grecians continued to plug away before English football's top goalscorer Jordan Rhodes fired home his 30th of the season with five minutes to go.
Paul Tisdale made a number of changes from the side that beat Bury last Saturday with 19-year-old Aaron Dawson
making his City debut at right-back in place of the injured Steve Tully.
Elsewhere Richard Logan dropped to the bench and there was a return to the starting line up for Liam Sercombe. John O'Flynn and Richard Duffy missed out through injury.
It meant that City could boast three products of their Centre Of Excellence in the starting line-up: Liam Sercombe, Scot Bennett and Dawson. New signing Luke O'Brien was named on the bench.
The Grecians pulled off the most memorable of victories at the Galpharm last season and they started the match with real intent as they looked to repeat that feat. David Noble was first to try his luck with a 35 yard free kick that flew just inches wide of the post before former Cardiff City striker Alan Lee glanced a very presentable chance wide from close range.
On six minutes a City breakaway via Jake Taylor down the right-hand side saw the Welshman try his luck but his effort was straight at former England Under 19 keeper Alex Smithies.Smithies was in action again on 10 minutes to keep out a decent attempt from Sercombe. Winning the ball 20 yards out, City's number seven got a first time shot away but the keeper palmed it away as it bounced just infront of him.
Artur Krysiak put in one of his best City performances at this venue last season and he was called into action on 30 minutes when hot-shot Rhodes met the impressive Jack Hunt's cross.
Nardiello then tried to catch out Smithies with a long distance effort with his right foot that was parried away, City's third real shot on target.
City had certainly held their own for the first half hour. Despite a lot of pressure they were coping well with Simon Grayson's new side.
On 40 minutes though the home side made the breakthrough with an effort Krysiak could do nothing about. Danny Ward was fouled and the former Bolton man picked himself up and swung a deep ball into the box from the left-hand side which was met by the rising figure of McCombe who nodded the ball into the far corner.
Half time came and went and the Grecians continued to work hard all across the pitch and Nardiello felt he should have been awarded a penalty when he went down under a challenge from Hunt as he prepared to shoot.
Dawson put in an impressive debut performance after being called upon at right-back following the injuries to Tully and Duffy. He came up against one of the league's most dangerous wingers in Gary Robertsand he was withdrawn just after the hour mark for last Saturday's goalscorer Logan. It meant Taylor moving to the right-back slot, showing once again the Reading loanee's versatility.
Rhodes who had netted hat-tricks against the Grecians on two previous occasions then bundled the ball home from close range after McCombe had flicked on a long throw but he saw his effort ruled out for offside.
The linesman's flag meant City, backed by 238 fans, were still in the match and they made another attacking change with Guillem Bauza coming on for Sercombe as the match moved into the final 20.
Noble then fired a free-kick over the wall but over the bar before the home side wrapped up the three points on 85 minutes. Oscar Gobern robbed the ball off the City midfield and fed Rhodes who didn't need a second invitation as he rifled a shot home.