Both sides were unbeaten going into the contest, but it was the Blues who emerged with that record still intact.
The goals arrived in the second half, with Ronan Curtis continuing his fine start to the campaign by providing a couple of assists.
He teed-up Hawkins for his first goal of the season and then helped Lowe extend the advantage further.
Matt Godden reduced the deficit in stoppage-time, but the visitors held on to secure another three-point haul.
Kenny Jackett made two changes from the side that drew with Shrewsbury on home soil the previous week.
Curtis returned from Republic of Ireland international duty to replace the injured Andre Green wide on the left.
The other switch came in the centre of midfield, where Ben Thompson dropped to the bench to make way for Ben Close.
Both sets of fans – including more than 2,500 from the south coast – contributed to a vibrant atmosphere as the game began at a breathless pace.
It was a hectic end-to-end affair, although neither goalkeeper was given much to do in the opening 45 minutes.
An early Christian Burgess header was blocked, while Rhys Bennett hooked over at the other end after Jason Cummings had flicked on Colin Daniel’s delivery.
Hawkins then did well to get on the end of a teasing Lee Brown cross and head narrowly over the bar.
The Peterborough coaching team had found reason to berate the fourth official and referee Roger East gave Steve Evans a ticking off.
But even they did not seem to think anything was amiss when Siriki Dembele went down in the box and half-hearted penalty appeals emerged from the stands.
Posh keeper Aaron Chapman was called into action for the first time midway through the first half and comfortably dealt with a long-range Evans effort.
There was a better opportunity at the other end moments later, with Cummings wastefully firing over when the ball fell kindly to him in the box.
Craig MacGillivray then got down at his near post to keep out a low angled drive from Jason Naismith.
Pompey finished the half brightly, but were lacking a decent final pass and with no time added on, the sides went in level at the break.
Peterborough United 0
While the first half had started frantically, there was a more measured approach from both sides when the action restarted.
Evans saw a shot blocked from the edge of the area, while MacGillivray commandingly claimed a Dembele free-kick.
That was for a foul on Cummings by Nathan Thompson, a challenge that earned the right-back the game’s first yellow card.
There was a nervy moment when MacGillivray failed to hold a cross from Naismith, but he gratefully gathered at the second attempt.
And it was the visiting army of fans that were celebrating when the Blues broke the deadlock just past the hour mark.
HAWKINS has been in excellent form so far this season and he opened his goalscoring account by meeting Curtis’ cross and guiding home a header.
Pompey then appealed for a penalty when Lowe’s strike hit Ivan Toney on the arm, although it would have been difficult for the Posh substitute to get out of the way.
It mattered not, though, as the visitors did double the advantage just seconds later, with Curtis providing another assist.
He headed Hawkins’ cross back into the mixer and a first-time finish from LOWE nestled comfortably in the net.
There were a smattering of bookings late on as tempers began to fray, but the Blues were looking solid at the back.
Curtis took a knock and limped off towards the end, while seven minutes of added time gave the hosts hope of a comeback.
That grew when Godden took advantage of some sloppy defending to pull one back, but Pompey saw out the closing stages to climb above Peterborough and into top spot.
Peterborough (4-1-2-1-2): Chapman; Naismith, Bennett, Tafazolli, Daniel; Woodyard (c); Ward (Maddison 72), Dembele; O’Hara (Walker 66); Cummings (Toney 59), Godden
Goals: Godden 90+4
Booked: Daniel, Walker
Subs not used: Tyler, Yorwerth, Cooper, Reed
Pompey (4-2-3-1): MacGillivray; N.Thompson, Burgess, Clarke, Brown; Close (B.Thompson 86), Naylor; Lowe, Evans (c), Curtis (Haunstrup 90); Hawkins
Goals: Hawkins 62, Lowe 75
Booked: N.Thompson, Hawkins, Close, Burgess
Subs not used: McGee, Rose, Wheeler, Pitman, Mason
Referee: Roger East
Attendance: 10,472 (2,513 Pompey fans)