The game appeared to have been heading towards a stalemate before Anderton's left foot strike at the far post, a goal that earned Rovers just their second away victory of the season.
Defeat means Town have now taken just one point from 12 and slipped to seventh position in the table with 15 games played.
Simon Weaver made two changes to the side that fell to the 3-2 defeat at Hartlepool last week. Back into the side came fit again Alex Pattison and Connor Hall, replacing Ryan Fallowfield and Lloyd Kerry.
For Rovers, Joey Barton made three changes as they looked to bounce back from a 3-1 home defeat to Newport County a week ago. Out went Nick Anderton, Alfie Kilgour and Aaron Collins with Paul Coutts, Cian Harries and Junior Brown coming into the line-up.
Town registered the fist opportunity of the game when Jack Muldoon was played through beyind the visitors defence but former Town man James Belshaw was alert enough to race off his line to smother the danger.
He was against tested in the eighth minute when George Thomson took aim from long range but Belshaw managed to recover the effort at the second attempt.
Rovers were dealt a blow on 10 minutes when leading scorer Brett Pitman was forced off through injury and replaced by Kilgour.
Will Smith was the first name in referee Wright's book when he pulled back his opponent just inside the Town half.
Neither side managed to find their feet early in the game with Rovers packing men behind the ball, mindful perhaps of their struggles away from home that has seen the triumph just once on their travels.
Former Ireland international Glenn Whelan followed Smith in the book for a late challenge on Lewis Page. From the resulting free-kick Thomson teased a ball into the box that was just inches away from the Town contingent at the far post.
A quiet period to the game was broken on the half-four when Muldoon fashioned himself some space but he couldn't keep shot on target to test Belshaw.
The best opportunity of the first-half would fall to Rovers though. Five minutes before the break a rare break forward down Town's right saw a low whipped cross delivered from Luke Thomas was cleared from under his crossbar by Page when a goal seemed all but certain.
Barton made his second change at the break with Anderton replacing Brown.
The second-half began in a similar vein to the opening 45 minutes with both sides adopting a solid set-up, but wary of committing too much forward in order to protect the stalemate.
Although there was a lack of goalmouth action the referee was kept busy and he showed his fourth yellow card of the day to Antony Evans as a result of his wholehearted challenge on Josh Falkingham, who was making his 200th Town appearance.
Having gone into the book Evans almost immediately redeemed himself with a long range volley that Mark Oxley did well to palm away to safety.
Rovers went ahead shortly after though when Anderton was first to the ball at the far post to knock home Kilgour's header.
Stung from conceding the game's opening goal Weaver immediately summoned Simon Power and Danilo Orsi from the bench in place of Thomson and Muldoon.
Aaron Martin was then introduced for his fourth appearance of the season when he replaced the injured Luke Armstrong.
Thomas almost doubled the visitors lead with ten minutes remaining when he outpaced Falkingham to get into the box but the Town skipper was quick to recover and put in a goal-saving tackle.
Town responded though with the clock beginning to tick down. Power's pace got him beyond Anderton but his cross was met by a Rovers head and the danger averted.
Evans almost added a second in injury time when his powerful effort had to be parried wide by Oxley.
Town have a break from league action next weekend when Wrexham are the visitors in the first round of the FA Cup.
TOWN: Oxley, Burrell, Page, Hall, Thomson, Falkingham Pattison, Diamond, Muldoon, Armstrong.
Subs not used: Cracknell, Sheron, Kerry, Power, Orsi, Martin.
Booked: Smith (13)
Bristol Rovers: Belshaw, Thomas (Collins, 90), Nicholson, Coutts, Taylor, Amderson, Evans. Harries. Whelan,
Brown (Anderton, 45), Pitman (Kilgour, 10)
Subs not used: Westbrooke, Martinez, Ward, Langlais.
Goal: Anderton (64)
Booked: Whelan (22), Brown (34), Evans (57), Coutts (88)
Referee: Peter Wright
Attendance: 2,614 (including 600 away fans)