The 19-year-old attacking midfielder, who netted an impressive solo effort in Saturday's 3-0 triumph over Harrogate Town, was on target again for the Gas with a curling second-half strike at the Memorial Stadium.
Rovers manager Joey Barton, who spent four years at Newcastle as a player between 2007 and 2011, heaped high praise on Anderson - who received a call-up to the Scotland under-21 squad last week - comparing the teenager to World Cup winner Diego Maradona.
Barton's side have now moved into the League Two play-off spots, three points adrift of second-placed Northampton Town.
Elsewhere, central midfielder Jack Young was involved in League One action for Wycombe Wanderers as the Chairboys claimed a dramatic 1-0 win against Fleetwood Town.
Young made an appearance from the substitutes' bench, replacing Lewis Wing in the 71st minute, before Gareth Ainsworth's side broke the deadlock in stoppage-time, courtesy of Jason McCarthy's strike and move within one point of the play-off spots in the English third tier.
Joe White, who signed a new three-year contract with Newcastle on Tuesday, was also in action for Hartlepool United, playing the full 90 minutes as Graeme Lee's men fell to a 2-0 home defeat against Bradford City, their first League Two loss at Victoria Park since November.
Goalkeeper Freddie Woodman was an unused substitute for AFC Bournemouth as Scott Parker's Cherries were held to a 1-1 draw against Reading at the Vitality Stadium while defender Kell Watts also watched from the sidelines as League One title challengers Wigan Athletic recorded a 2-0 away win at Crewe Alexandra.
And left-back Matty Bondswell could only look on from the bench as Shrewsbury Town recorded a 5-0 hammering at home to Morecambe while Matty Longstaff sat out Mansfield Town's 3-1 away defeat against Port Vale due to a minor injury.