The result sees Barca equal the longest unbeaten run in the division's history, which was set by Real Sociedad during the 1978-79 and 79-80 campaigns, and they can break it when they play host to Valencia next weekend.
Aspas made it 2-0 after 57 minutes before netting his second three minutes later.
Messi opened the scoring with a fine free-kick, struck his second before half-time and sealed the win in the closing stages with his 39th goal of the season in all competitions after Nabil El Zhar had pulled one back.
Barca to win to nil is priced at 8/15 (1.53), although more appealing is the price of 9/10 (1.90) for Valverde's side to win with a -2 handicap. Left back Jordi Alba has undergone the most dramatic transformation under Valverde after falling out of favour under Luis Enrique, and has developed a particularly profitable understanding with Messi.
Saturday brought yet another change in position as Roberto showed again just how important he is to the Barcelona team.
Ousmane Dembele claims to not feel "any pressure" at Barcelona despite living the dream alongside iconic figures such as Lionel Messi.More news: Man drives van into restaurant in Germany, killing two plus himself
More news: A Chilly & Mostly Sunny Finish to the Weekend
More news: Roma shock Barcelona to join list of greatest Champions League comebacks
Messi was undoubtedly the best player on the pitch, but Philippe Coutinho also impressed throughout for Barcelona. "It has been quite hard, because of the fact it's an old record that hasn't been broken for a long time". They are seven games short of becoming the first team to complete a 38-game Liga season unbeaten.
Barcelona's defence has been their great strength, but there's no doubting the team switched off after going two goals up.
However, Barcelona failed to heed the warning and were deservedly punished at the 68-minute mark when Gabriel beat Gerard Pique and found El Zhar, who fired past goalkeeper Marc-Andre ter Stegen.
Barca are next in action on Wednesday at Roma in the Champions League quarter-final second leg, defending a 4-1 advantage from the first leg at the Nou Camp.
It's suggested Villarreal and Celta Vigo are also keen.