Tomlinson on target as Gainsborough Trinity beaten by Boston United
Craig Elliott's Pilgrims got the better of the hosts - whose starting XI featured ex-Pilgrims Simon Ainge, Martyn Woolford and Gregg Smith - at the Northolme.
Trinity stopper Tom Jackson had to be alert to deny United's Jordan Thewlis within the opening 25 seconds of the contest.
Summer signing Green announced his arrival with his first goal in United colours on 12 minutes, sweeping home a driven cross.
Jordan Archer, who followed Paul Green into the club, almost got in on the act seconds later, but Jackson pulled off another impressive save.
The Trinity number one was at it again to keep out Connor Dimaio's long-range free kick, also denying the same player's powerful drive and thwarting Thewlis once more.
Despite Jackson's first-half heroics, the Pilgrims' lead was doubled seconds into the second half as Jordan Burrow was on target for his new club, forcing home Jay Rollins' cross with a diving header.
Tomlinson got on the scoresheet in the 73rd-minute, prodding home after nipping in between Peter Crook and Scott Garner.
Substitute Jack Walters forced a save from United keeper Crook as Curtis Woodhouse's side attempted to claw themselves level, with United's Rollins seeing a struike rebound off the underside of the bar at the other end.
TRINITY: Jackson, Dixon, Trialist, Williamson, Ainge, Woolford, Orlando-Young, Collins, Smith, Tomlinson, Fyfe; Subs (not used): Dennison, Leverton, Bucci, Trialist, Walters.
PILGRIMS: First half - Fitzsimons, Tootle, Shiels, Garner, Askew, Green, Platt, Dimaio, Thewlis, Archer, Hawkridge; Second half - Crook, Warren, Garner, Duxbury, Gibbens, Green (Trialist B 58), Thanoj, Dimaio (Trialist C 58), Rollins, Burrow, Trialist A.