Defender Matt Mills gave winless Wanderers the lead but Brighton fought back strongly to leave Dougie Freedman's men with only one point from their first four Sky Bet Championship games.
The Seagulls, who gave a full debut to Aston Villa loanee Joe Bennett and home starts to Portuguese playmaker Teixeira and Dutch midfielder Danny Holla, started well and Spaniard Bruno Saltor should have hit the target early on.
Teixeira, on loan from Liverpool, and Jake Forster-Caskey lined up well on the flank and Bruno drove over wastefully from outside the area.
Forster-Caskey fired over the bar for Brighton before the hosts had a let-off in the 15th minute when South Korean Chung-Yong Lee wasted a fine opening.
Lee blazed a half volley over from 15 yards after Inigo Calderon lost possession allowing Craig Davies to deliver a decent ball into the box.
Brighton, buoyant following their first win of the season at Leeds in midweek, survived another scare seven minutes later when experienced central defender David Wheater headed over following a corner by skipper Jay Spearing.
But Bolton's pressure was rewarded on 25 minutes with former Leicester defender Mills leaping to splendidly to head home a free-kick from Spearing.
Bolton goalkeeper Adam Bogdan produced a fingertip save to preserve his side's lead, tipping a fierce angled drive from Mackail-Smith onto the bar.
The Seagulls continued to threaten and record signing Mackail-Smith muscled into the six-yard box to thump home an equaliser on 37 minutes from Calderon's fine cross.
Hungarian keeper Bogdan took a blow to the head from Mackail-Smith as the ball went in and was replaced by former Leeds man Andy Lonergan.
Brighton piled on pressure before the break and defender Lewis Dunk had a header cleared off the line by Spearing after skipper Gordon Greer's goal-bound shot was parried by Lonergan at the near post.
The Seagulls' defence switched off shortly after the break when Joe Mason headed down into the path of Craig Davies, but the Welshman wastefully shot wide with only keeper David Stockdale to beat.
Mackail-Smith came close to putting Brighton ahead on the hour with an overhead kick which flew wide after Bennett's ball into the area.
Brighton's second goal did, however, arrive in the 64th minute when Teixeira netted his second goal in successive games through the legs of Lonergan from a pass by Bennett.
Bolton, now without a clean sheet in five league and cup games this season, struggled to get back into the game as Albion substitute Kazenga LuaLua had a low free-kick blocked.
LuaLua later set up the hard-working Mackail-Smith but the former Peterborough marksman fired wide with only Lonergan to beat.