United looked set to draw level with the Canaries at the summit on Saturday after two goals from Luciano Becchio had put them 2-1 up at Victoria Park, but Sweeney powered in a 93rd-minute header to keep the visitors two points adrift.
Argentinian striker Becchio saw his looping header expertly tipped onto the crossbar by Scott Flinders before he scored after 23 minutes, turning home Jermaine Beckford's deft chip from 12 yards.
But battling Pool hit back after the break and Adam Boyd levelled in the 71st minute, cracking home an unstoppable low volley from 20 yards.
Becchio, however, appeared to have the final say seven minutes later when Flinders flapped at a corner, Lubo Michalik's header hit the bar and he tapped in from close range.
But Sweeney's powerful far-post header from six yards after Boyd had flicked on a Ritchie Jones free-kick earned a deserved point for the hosts.