Thanoj's first half free-kick and second half header put the Pilgrims firmly in control and they secured all three points despite George Newell reducing the arrears with 11 minutes to play.
Luke Shiels' 88th minute header sealed maximum spoils on the road for Craig Elliott's side.
Fit-again Thanoj was one of three players coming into Elliott’s starting XI, alongside Alex Whittle and Martyn Woolford.
Southport had the clearer openings early on, with Reagan Ogle heading wide and Shiels being required to head clear at the back post to deny Devarn Green.
United responded positively and Shiels’ glancing header flew wide from a Woolford corner, while Jordan Thewlis threaded Dominic Knowles into the clear, but his effort flashed wide of the near post.
Thanoj was denied by a brave Zehn Mohammed block, before clipping the outside of the post with a 20-yard free-kick.
Mohammed went close to handing Port the lead, but hooked an effort narrowly wide following an Ogle long throw.
United broke the deadlock in the 44th minute when David Morgan was penalised for a foul and THANOJ stepped up to bend home the resulting free-kick from 20 yards.
Crook made a miraculous double save at the beginning of the second half, denying Green on the angle before somehow thwarting Sampson on the follow-up. Crook then denied Mohammed from the resulting corner.
Sampson cleared off the line from Knowles before the Pilgrims doubled their lead on the hour mark. Brad Abbott played Woolford into a crossing position and he chopped the ball back onto his right foot before delivering a pinpoint centre for THANOJ to head home from close-range.
Thanoj should have completed a hat-trick moments later, but curled another free-kick a fraction too high.
Home keeper Charlie Albinson denied Tom Platt from distance before Southport struck, with NEWELL heading home following Ogle’s long throw-in.
United’s nerves were calmed two minutes from time when Thanoj’s deep corner was powered home by the head of SHIELS at the back post.
Southport (4-4-2): Charlie Albinson; Zehn Mohammed, Charlie Oliver, Ryan Astles, Reagan Ogle; Devarn Green (Connor Woods 77), David Morgan, Russell Benjamin, Brad Bauress (Morgan Homson-Smith 80); Jack Sampson, George Newell. Subs (not used): Andy Parry, Dean Winnard.
Boston (4-3-3): Peter Crook; Alex Penny, Luke Shiels, Scott Garner, Alex Whittle (Ashley Jackson 90); Brad Abbott, Tom Platt, Andi Thanoj (Jonathan Wafula 90); Jordan Thewlis, Dominic Knowles (Jay Rollins 90), Martyn Woolford. Subs (not used): Simon Ainge, George Willis (gk).
Referee: Aaron Bannister.
Attendance: 883.