Boro' progressed in the FA Trophy south Hampshire derby clash thanks to a goal from the evergreen Steve Claridge and a string of superb saves from Nathan Ashmore.
It was Claridge, who signed just before Friday's deadline, who netted the winner as the 45 year-old rolled back the years but Pike's other new signing Nathan Ashmore pulled off a string of saves that denied Sholing an equaliser.
After a slow start it was Gosport who settled first with Justin Bennett denied by Lee Webber with the striker closing in.
Former Boro' man Kevin Brewster then went close for the visitors before Dan Wooden and Adam Wilde created a chance for Brett Poate but his shot fizzed just over.
After a quiet start, the headline makers job was made easy as Bennett carved an opening and Claridge's neat turn and fierce drive beat Webber and raced into the far corner of the net.
With Gosport looking the more lively, Gavin Jones and Claridge then combined to open up the visitors but a superb, last gasp challenge from Adam Camfield denied Bennett Boro's second.
But with all the pre-match focus on Claridge, it was Boro's other new man Nathan Ashmore who would catch the eye. Just before the break he pulled out a special save to deny Bryon Mason from close range.
Then, with Sholing fired up for the second period, he continued to deny the visitors with an even better save low down to deny Mike Carter.
As Gosport struggled to hold on to the slender lead, Ashmore finger-tipped Iain Seabrook's free-kick over and found himself under increasing pressure as Boro's defence strained.
With the pressure over, Borough came charging back with the Jones' - Ian and Gavin - combining to set up Bennett to head just over.
Sholing then thought they had levelled as Lee Wort finally beat Ashmore with a lob but celebrations were cut short when the referee spotted the linesman's raised flag.
Boro' will now go into the draw for the second qualifying round which will be played on Saturday 5th November.
